diff --git a/sprout/complex/complex.hpp b/sprout/complex/complex.hpp
index 231b2b31..0df9718e 100644
--- a/sprout/complex/complex.hpp
+++ b/sprout/complex/complex.hpp
@@ -40,8 +40,8 @@ namespace sprout {
 		typedef typename array_type::size_type size_type;
 		typedef typename array_type::pointer pointer;
 		typedef typename array_type::const_pointer const_pointer;
-		typedef typename array_type::pointer reverse_iterator;
-		typedef typename array_type::pointer const_reverse_iterator;
+		typedef typename array_type::reverse_iterator reverse_iterator;
+		typedef typename array_type::const_reverse_iterator const_reverse_iterator;
 	public:
 		SPROUT_STATIC_CONSTEXPR size_type static_size = array_type::static_size;
 	private:
diff --git a/sprout/math/quaternion.hpp b/sprout/math/quaternion.hpp
index e9d38952..b4b682c5 100644
--- a/sprout/math/quaternion.hpp
+++ b/sprout/math/quaternion.hpp
@@ -8,1521 +8,8 @@
 #ifndef SPROUT_MATH_QUATERNION_HPP
 #define SPROUT_MATH_QUATERNION_HPP
 
-#include <iosfwd>
-#include <sstream>
-#include <locale>
 #include <sprout/config.hpp>
-#include <sprout/math/abs.hpp>
-#include <sprout/math/cos.hpp>
-#include <sprout/math/sin.hpp>
-#include <sprout/math/cosh.hpp>
-#include <sprout/math/exp.hpp>
-#include <sprout/math/abs.hpp>
-//#include <sprout/math/sinc.hpp>
-//#include <sprout/math/sinhc.hpp>
-#include <sprout/complex/complex.hpp>
-#include <sprout/range/algorithm/max_element.hpp>
-#include <sprout/range/numeric/accumulate.hpp>
-
-namespace sprout {
-	namespace math {
-		namespace detail {
-			template<typename T>
-			class abs_less {
-			public:
-				SPROUT_CONSTEXPR T
-				operator()(T const& lhs, T const& rhs) const {
-					return sprout::math::abs(lhs) < sprout::math::abs(rhs);
-				}
-			};
-			template<typename T>
-			class abs_plus {
-			public:
-				SPROUT_CONSTEXPR T
-				operator()(T const& lhs, T const& rhs) const {
-					return sprout::math::abs(lhs) + sprout::math::abs(rhs);
-				}
-			};
-			template<typename T, std::size_t N>
-			SPROUT_CONSTEXPR T
-			abs_max(sprout::array<T, N> const& c) {
-				return sprout::math::abs(*sprout::range::max_element(c, sprout::math::detail::abs_less<T>()));
-			}
-			template<typename T, std::size_t N>
-			SPROUT_CONSTEXPR T
-			sum(sprout::array<T, N> const& c) {
-				return sprout::range::accumulate(c, static_cast<T>(0));
-			}
-			template<typename T, std::size_t N>
-			SPROUT_CONSTEXPR T
-			abs_sum(sprout::array<T, N> const& c) {
-				return sprout::range::accumulate(c, static_cast<T>(0), sprout::math::detail::abs_plus<T>());
-			}
-			template<typename T>
-			SPROUT_CONSTEXPR sprout::array<T, 2>
-			mul(sprout::array<T, 2> const& l, T const& r) {
-				return sprout::array<T, 2>{{
-					l[0] * r,
-					l[1] * r,
-					}};
-			}
-			template<typename T>
-			SPROUT_CONSTEXPR sprout::array<T, 2>
-			mul(sprout::array<T, 2> const& l, sprout::array<T, 2> const& r) {
-				return sprout::array<T, 2>{{
-					l[0] * r[0],
-					l[1] * r[1],
-					}};
-			}
-			template<typename T>
-			SPROUT_CONSTEXPR sprout::array<T, 4>
-			mul(sprout::array<T, 4> const& l, T const& r) {
-				return sprout::array<T, 4>{{
-					l[0] * r,
-					l[1] * r,
-					l[2] * r,
-					l[3] * r
-					}};
-			}
-			template<typename T>
-			SPROUT_CONSTEXPR sprout::array<T, 4>
-			mul(sprout::array<T, 4> const& l, sprout::array<T, 4> const& r) {
-				return sprout::array<T, 4>{{
-					l[0] * r[0],
-					l[1] * r[1],
-					l[2] * r[2],
-					l[3] * r[3]
-					}};
-			}
-		}	// namespace detail
-
-#define	SPROUT_QUATERNION_ACCESSOR_GENERATOR(type) \
-			SPROUT_CONSTEXPR type real() const { \
-				return (a); \
-			} \
-			SPROUT_CONSTEXPR quaternion<type> unreal() const { \
-				return (quaternion<type>(static_cast<type>(0), b, c, d)); \
-			} \
-			SPROUT_CONSTEXPR type R_component_1() const { \
-				return (a); \
-			} \
-			SPROUT_CONSTEXPR type R_component_2() const { \
-				return (b); \
-			} \
-			SPROUT_CONSTEXPR type R_component_3() const { \
-				return (c); \
-			} \
-			SPROUT_CONSTEXPR type R_component_4() const { \
-				return (d); \
-			} \
-			SPROUT_CONSTEXPR sprout::complex<type> C_component_1() const { \
-				return sprout::complex<type>(a, b); \
-			} \
-			SPROUT_CONSTEXPR sprout::complex<type> C_component_2() const { \
-				return sprout::complex<type>(c, d); \
-			}
-
-#define	SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(type) \
-			template<typename X> \
-			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator=(quaternion<X> const& a_affecter) { \
-				a = static_cast<type>(a_affecter.R_component_1()); \
-				b = static_cast<type>(a_affecter.R_component_2()); \
-				c = static_cast<type>(a_affecter.R_component_3()); \
-				d = static_cast<type>(a_affecter.R_component_4()); \
-				return *this; \
-			} \
-			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator=(quaternion<type> const& a_affecter) { \
-				a = a_affecter.a; \
-				b = a_affecter.b; \
-				c = a_affecter.c; \
-				d = a_affecter.d; \
-				return *this; \
-			} \
-			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator=(type const& a_affecter) { \
-				a = a_affecter; \
-				b = c = d = static_cast<type>(0); \
-				return *this; \
-			} \
-			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator=(sprout::complex<type> const& a_affecter) { \
-				a = a_affecter.real(); \
-				b = a_affecter.imag(); \
-				c = d = static_cast<type>(0); \
-				return *this; \
-			}
-
-#define	SPROUT_QUATERNION_MEMBER_DATA_GENERATOR(type) \
-			type a; \
-			type b; \
-			type c; \
-			type d;
-
-		//
-		// quaternion
-		//
-		template<typename T>
-		class quaternion {
-		public:
-			typedef T value_type;
-		protected:
-			SPROUT_QUATERNION_MEMBER_DATA_GENERATOR(T)
-		public:
-			explicit SPROUT_CONSTEXPR quaternion(
-				T const& requested_a = T(),
-				T const& requested_b = T(),
-				T const& requested_c = T(),
-				T const& requested_d = T()
-				)
-				: a(requested_a)
-				, b(requested_b)
-				, c(requested_c)
-				, d(requested_d)
-			{}
-			explicit SPROUT_CONSTEXPR quaternion(
-				sprout::complex<T> const& z0,
-				sprout::complex<T> const& z1 = sprout::complex<T>()
-				)
-				: a(z0.real())
-				, b(z0.imag())
-				, c(z1.real())
-				, d(z1.imag())
-			{}
-			template<typename X>
-			explicit SPROUT_CONSTEXPR quaternion(quaternion<X> const& a_recopier)
-				: a(static_cast<T>(a_recopier.R_component_1()))
-				, b(static_cast<T>(a_recopier.R_component_2()))
-				, c(static_cast<T>(a_recopier.R_component_3()))
-				, d(static_cast<T>(a_recopier.R_component_4()))
-			{}
-			SPROUT_QUATERNION_ACCESSOR_GENERATOR(T)
-			SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(T)
-			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator+=(T const& rhs) {
-				T at = a + rhs;
-				a = at;
-				return *this;
-			}
-			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator+=(sprout::complex<T> const& rhs) {
-				T at = a + rhs.real();
-				T bt = b + rhs.imag();
-				a = at; 
-				b = bt;
-				return *this;
-			}
-			template<typename X>
-			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator+=(quaternion<X> const& rhs) {
-				T at = a + static_cast<T>(rhs.R_component_1());
-				T bt = b + static_cast<T>(rhs.R_component_2());
-				T ct = c + static_cast<T>(rhs.R_component_3());
-				T dt = d + static_cast<T>(rhs.R_component_4());
-				a = at;
-				b = bt;
-				c = ct;
-				d = dt;
-				return *this;
-			}
-			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator-=(T const& rhs) {
-				T at = a - rhs;
-				a = at;
-				return *this;
-			}
-			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator-=(sprout::complex<T> const& rhs) {
-				T at = a - rhs.real();
-				T bt = b - rhs.imag();
-				a = at;
-				b = bt;
-				return *this;
-			}
-			template<typename X>
-			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator-=(quaternion<X> const& rhs) {
-				T at = a - static_cast<T>(rhs.R_component_1());
-				T bt = b - static_cast<T>(rhs.R_component_2());
-				T ct = c - static_cast<T>(rhs.R_component_3());
-				T dt = d - static_cast<T>(rhs.R_component_4());
-				a = at;
-				b = bt;
-				c = ct;
-				d = dt;
-				return *this;
-			}
-			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator*=(T const& rhs) {
-				T at = a * rhs;
-				T bt = b * rhs;
-				T ct = c * rhs;
-				T dt = d * rhs;
-				a = at;
-				b = bt;
-				c = ct;
-				d = dt;
-				return *this;
-			}
-			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator*=(sprout::complex<T> const& rhs) {
-				T ar = rhs.real();
-				T br = rhs.imag();
-				T at = +a * ar - b * br;
-				T bt = +a * br + b * ar;
-				T ct = +c * ar + d * br;
-				T dt = -c * br + d * ar;
-				a = at;
-				b = bt;
-				c = ct;
-				d = dt;
-				return *this;
-			}
-			template<typename X>
-			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator*=(quaternion<X> const& rhs) {
-				T ar = static_cast<T>(rhs.R_component_1());
-				T br = static_cast<T>(rhs.R_component_2());
-				T cr = static_cast<T>(rhs.R_component_3());
-				T dr = static_cast<T>(rhs.R_component_4());
-				T at = +a * ar - b * br - c * cr - d * dr;
-				T bt = +a * br + b * ar + c * dr - d * cr;
-				T ct = +a * cr - b * dr + c * ar + d * br;
-				T dt = +a * dr + b * cr - c * br + d * ar;
-				a = at;
-				b = bt;
-				c = ct;
-				d = dt;
-				return *this;
-			}
-			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator/=(T const& rhs) {
-				T at = a / rhs;
-				T bt = b / rhs;
-				T ct = c / rhs;
-				T dt = d / rhs;
-				a = at;
-				b = bt;
-				c = ct;
-				d = dt;
-				return *this;
-			}
-			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator/=(sprout::complex<T> const& rhs) {
-				T ar = rhs.real();
-				T br = rhs.imag();
-				T denominator = ar * ar + br * br;
-				T at =(+a * ar + b * br) / denominator;
-				T bt =(-a * br + b * ar) / denominator;
-				T ct =(+c * ar - d * br) / denominator;
-				T dt =(+c * br + d * ar) / denominator;
-				a = at;
-				b = bt;
-				c = ct;
-				d = dt;
-				return *this;
-			}
-			template<typename X>
-			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator/=(quaternion<X> const& rhs) {
-				T ar = static_cast<T>(rhs.R_component_1());
-				T br = static_cast<T>(rhs.R_component_2());
-				T cr = static_cast<T>(rhs.R_component_3());
-				T dr = static_cast<T>(rhs.R_component_4());
-				T denominator = ar * ar + br * br + cr * cr + dr * dr;
-				T at =(+a * ar + b * br + c * cr + d * dr) / denominator;
-				T bt =(-a * br + b * ar - c * dr + d * cr) / denominator;
-				T ct =(-a * cr + b * dr + c * ar - d * br) / denominator;
-				T dt =(-a * dr - b * cr + c * br + d * ar) / denominator;
-				a = at;
-				b = bt;
-				c = ct;
-				d = dt;
-				return *this;
-			}
-		};
-
-		template<>
-		class quaternion<float>;
-		template<>
-		class quaternion<double>;
-		template<>
-		class quaternion<long double>;
-
-#define	SPROUT_QUATERNION_CONSTRUCTOR_GENERATOR(type) \
-			explicit SPROUT_CONSTEXPR quaternion( \
-				type const& requested_a = static_cast<type>(0), \
-				type const& requested_b = static_cast<type>(0), \
-				type const& requested_c = static_cast<type>(0), \
-				type const& requested_d = static_cast<type>(0) \
-				) \
-				: a(requested_a) \
-				, b(requested_b) \
-				, c(requested_c) \
-				, d(requested_d) \
-			{} \
-			explicit SPROUT_CONSTEXPR quaternion( \
-				sprout::complex<type> const& z0, \
-				sprout::complex<type> const& z1 = sprout::complex<type>() \
-				) \
-				: a(z0.real()) \
-				, b(z0.imag()) \
-				, c(z1.real()) \
-				, d(z1.imag()) \
-			{}
-
-#define	SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_1(type) \
-			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator+=(type const& rhs) { \
-				a += rhs; \
-				return *this; \
-			}
-
-#define	SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_2(type) \
-			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator+=(sprout::complex<type> const& rhs) { \
-				a += rhs.real(); \
-				b += rhs.imag(); \
-				return *this; \
-			}
-
-#define	SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_3(type) \
-			template<typename X> \
-			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator+=(quaternion<X> const& rhs) { \
-				a += static_cast<type>(rhs.R_component_1()); \
-				b += static_cast<type>(rhs.R_component_2()); \
-				c += static_cast<type>(rhs.R_component_3()); \
-				d += static_cast<type>(rhs.R_component_4()); \
-				return *this; \
-			}
-
-#define	SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_1(type) \
-			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator-=(type const& rhs) { \
-				a -= rhs; \
-				return *this; \
-			}
-
-#define	SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_2(type) \
-			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator-=(sprout::complex<type> const& rhs) { \
-				a -= rhs.real(); \
-				b -= rhs.imag(); \
-				return *this; \
-			}
-
-#define	SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_3(type) \
-			template<typename X> \
-			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator-=(quaternion<X> const& rhs) { \
-				a -= static_cast<type>(rhs.R_component_1()); \
-				b -= static_cast<type>(rhs.R_component_2()); \
-				c -= static_cast<type>(rhs.R_component_3()); \
-				d -= static_cast<type>(rhs.R_component_4()); \
-				return *this; \
-			}
-
-#define	SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_1(type) \
-			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator*=(type const& rhs) { \
-				a *= rhs; \
-				b *= rhs; \
-				c *= rhs; \
-				d *= rhs; \
-				return *this; \
-			}
-
-#define	SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_2(type) \
-			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator*=(sprout::complex<type> const& rhs) { \
-				type ar = rhs.real(); \
-				type br = rhs.imag(); \
-				type at = +a * ar - b * br; \
-				type bt = +a * br + b * ar; \
-				type ct = +c * ar + d * br; \
-				type dt = -c * br + d * ar; \
-				a = at; \
-				b = bt; \
-				c = ct; \
-				d = dt; \
-				return *this; \
-			}
-
-#define	SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_3(type) \
-			template<typename X> \
-			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator*=(quaternion<X> const& rhs) { \
-				type ar = static_cast<type>(rhs.R_component_1()); \
-				type br = static_cast<type>(rhs.R_component_2()); \
-				type cr = static_cast<type>(rhs.R_component_3()); \
-				type dr = static_cast<type>(rhs.R_component_4()); \
-				type at = +a * ar - b * br - c * cr - d * dr; \
-				type bt = +a * br + b * ar + c * dr - d * cr; \
-				type ct = +a * cr - b * dr + c * ar + d * br; \
-				type dt = +a * dr + b * cr - c * br + d * ar; \
-				a = at; \
-				b = bt; \
-				c = ct; \
-				d = dt; \
-				return *this; \
-			}
-
-#define	SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_1(type) \
-			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator/=(type const& rhs) { \
-				a /= rhs; \
-				b /= rhs; \
-				c /= rhs; \
-				d /= rhs; \
-				return *this; \
-			}
-
-#define	SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \
-			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator/=(sprout::complex<type> const& rhs) { \
-				sprout::array<type, 2> tr{{ \
-					rhs.real(), \
-					rhs.imag() \
-				}}; \
-				type mixam = static_cast<type>(1) / sprout::math::detail::abs_max(tr); \
-				tr = sprout::math::detail::mul(tr, mixam); \
-				sprout::array<type, 4> tt{{ \
-					+a * tr[0] + b * tr[1], \
-					-a * tr[1] + b * tr[0], \
-					+c * tr[0] - d * tr[1], \
-					+c * tr[1] + d * tr[0] \
-				}}; \
-				tr = sprout::math::detail::mul(tr, tr); \
-				tt = sprout::math::detail::mul(tt, mixam / sprout::math::detail::sum(tr)); \
-				a = tt[0]; \
-				b = tt[1]; \
-				c = tt[2]; \
-				d = tt[3]; \
-				return *this; \
-			}
-
-#define	SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_3(type) \
-			template<typename X> \
-			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator/=(quaternion<X> const& rhs) { \
-				sprout::array<type, 4> tr{{ \
-					static_cast<type>(rhs.R_component_1()), \
-					static_cast<type>(rhs.R_component_2()), \
-					static_cast<type>(rhs.R_component_3()), \
-					static_cast<type>(rhs.R_component_4()) \
-				}}; \
-				type mixam = static_cast<type>(1) / sprout::math::detail::abs_max(tr); \
-				tr = sprout::math::detail::mul(tr, mixam); \
-				sprout::array<type, 4> tt{{ \
-					+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] \
-				}}; \
-				tr = sprout::math::detail::mul(tr, tr); \
-				tt = sprout::math::detail::mul(tt, mixam / sprout::math::detail::sum(tr)); \
-				a = tt[0]; \
-				b = tt[1]; \
-				c = tt[2]; \
-				d = tt[3]; \
-				return *this; \
-			}
-
-#define	SPROUT_QUATERNION_MEMBER_ADD_GENERATOR(type) \
-		SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_1(type) \
-		SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_2(type) \
-		SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_3(type)
-
-#define	SPROUT_QUATERNION_MEMBER_SUB_GENERATOR(type) \
-		SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_1(type) \
-		SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_2(type) \
-		SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_3(type)
-
-#define	SPROUT_QUATERNION_MEMBER_MUL_GENERATOR(type) \
-		SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_1(type) \
-		SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_2(type) \
-		SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_3(type)
-
-#define	SPROUT_QUATERNION_MEMBER_DIV_GENERATOR(type) \
-		SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_1(type) \
-		SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \
-		SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_3(type)
-
-#define	SPROUT_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(type) \
-		SPROUT_QUATERNION_MEMBER_ADD_GENERATOR(type) \
-		SPROUT_QUATERNION_MEMBER_SUB_GENERATOR(type) \
-		SPROUT_QUATERNION_MEMBER_MUL_GENERATOR(type) \
-		SPROUT_QUATERNION_MEMBER_DIV_GENERATOR(type)
-
-		template<>
-		class quaternion<float> {
-		public:
-			typedef float value_type;
-		protected:
-			SPROUT_QUATERNION_MEMBER_DATA_GENERATOR(float)
-		public:
-			SPROUT_QUATERNION_CONSTRUCTOR_GENERATOR(float)
-			explicit SPROUT_CONSTEXPR quaternion(quaternion<double> const& a_recopier);
-			explicit SPROUT_CONSTEXPR quaternion(quaternion<long double> const& a_recopier);
-			SPROUT_QUATERNION_ACCESSOR_GENERATOR(float)
-			SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(float)
-			SPROUT_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(float)
-		};
-
-		template<>
-		class quaternion<double> {
-		public:
-			typedef double value_type;
-		protected:
-			SPROUT_QUATERNION_MEMBER_DATA_GENERATOR(double)
-		public:
-			SPROUT_QUATERNION_CONSTRUCTOR_GENERATOR(double)
-			explicit SPROUT_CONSTEXPR quaternion(quaternion<float> const& a_recopier);
-			explicit SPROUT_CONSTEXPR quaternion(quaternion<long double> const& a_recopier);
-			SPROUT_QUATERNION_ACCESSOR_GENERATOR(double)
-			SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(double)
-			SPROUT_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(double)
-		};
-
-		template<>
-		class quaternion<long double> {
-		public:
-			typedef double value_type;
-		protected:
-			SPROUT_QUATERNION_MEMBER_DATA_GENERATOR(long double)
-		public:
-			SPROUT_QUATERNION_CONSTRUCTOR_GENERATOR(long double)
-			explicit SPROUT_CONSTEXPR quaternion(quaternion<float> const& a_recopier);
-			explicit SPROUT_CONSTEXPR quaternion(quaternion<double> const& a_recopier);
-			SPROUT_QUATERNION_ACCESSOR_GENERATOR(long double)
-			SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(long double)
-			SPROUT_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(long double)
-		};
-
-		SPROUT_CONSTEXPR sprout::math::quaternion<float>::quaternion(sprout::math::quaternion<double> const& a_recopier)
-			: a(static_cast<float>(a_recopier.R_component_1()))
-			, b(static_cast<float>(a_recopier.R_component_2()))
-			, c(static_cast<float>(a_recopier.R_component_3()))
-			, d(static_cast<float>(a_recopier.R_component_4()))
-		{}
-		SPROUT_CONSTEXPR sprout::math::quaternion<float>::quaternion(sprout::math::quaternion<long double> const& a_recopier)
-			: a(static_cast<float>(a_recopier.R_component_1()))
-			, b(static_cast<float>(a_recopier.R_component_2()))
-			, c(static_cast<float>(a_recopier.R_component_3()))
-			, d(static_cast<float>(a_recopier.R_component_4()))
-		{}
-
-		SPROUT_CONSTEXPR sprout::math::quaternion<double>::quaternion(sprout::math::quaternion<float> const& a_recopier)
-			: a(static_cast<double>(a_recopier.R_component_1()))
-			, b(static_cast<double>(a_recopier.R_component_2()))
-			, c(static_cast<double>(a_recopier.R_component_3()))
-			, d(static_cast<double>(a_recopier.R_component_4()))
-		{}
-		SPROUT_CONSTEXPR sprout::math::quaternion<double>::quaternion(sprout::math::quaternion<long double> const& a_recopier)
-			: a(static_cast<double>(a_recopier.R_component_1()))
-			, b(static_cast<double>(a_recopier.R_component_2()))
-			, c(static_cast<double>(a_recopier.R_component_3()))
-			, d(static_cast<double>(a_recopier.R_component_4()))
-		{}
-
-		SPROUT_CONSTEXPR sprout::math::quaternion<long double>::quaternion(sprout::math::quaternion<float> const& a_recopier)
-			: a(static_cast<long double>(a_recopier.R_component_1()))
-			, b(static_cast<long double>(a_recopier.R_component_2()))
-			, c(static_cast<long double>(a_recopier.R_component_3()))
-			, d(static_cast<long double>(a_recopier.R_component_4()))
-		{}
-		SPROUT_CONSTEXPR sprout::math::quaternion<long double>::quaternion(sprout::math::quaternion<double> const& a_recopier)
-			: a(static_cast<long double>(a_recopier.R_component_1()))
-			, b(static_cast<long double>(a_recopier.R_component_2()))
-			, c(static_cast<long double>(a_recopier.R_component_3()))
-			, d(static_cast<long double>(a_recopier.R_component_4()))
-		{}
-
-#undef	SPROUT_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR
-#undef	SPROUT_QUATERNION_MEMBER_ADD_GENERATOR
-#undef	SPROUT_QUATERNION_MEMBER_SUB_GENERATOR
-#undef	SPROUT_QUATERNION_MEMBER_MUL_GENERATOR
-#undef	SPROUT_QUATERNION_MEMBER_DIV_GENERATOR
-#undef	SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_1
-#undef	SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_2
-#undef	SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_3
-#undef	SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_1
-#undef	SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_2
-#undef	SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_3
-#undef	SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_1
-#undef	SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_2
-#undef	SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_3
-#undef	SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_1
-#undef	SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_2
-#undef	SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_3
-#undef	SPROUT_QUATERNION_CONSTRUCTOR_GENERATOR
-#undef	SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR
-#undef	SPROUT_QUATERNION_MEMBER_DATA_GENERATOR
-#undef	SPROUT_QUATERNION_ACCESSOR_GENERATOR
-
-		//
-		// 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
-
-		//
-		// operator<<
-		// operator>>
-		//
-		template<typename T, typename Elem, typename Traits>
-		inline SPROUT_NON_CONSTEXPR std::basic_ostream<Elem, Traits>&
-		operator<<(	std::basic_ostream<Elem, Traits>& lhs, sprout::math::quaternion<T> const& rhs) {
-			std::basic_ostringstream<Elem, Traits> s;
-			s.flags(lhs.flags());
-			s.imbue(lhs.getloc());
-			s.precision(lhs.precision());
-			s
-				<< '('
-				<< rhs.R_component_1() << ','
-				<< rhs.R_component_2() << ','
-				<< rhs.R_component_3() << ','
-				<< rhs.R_component_4()
-				<< ')'
-				;
-			return lhs << s.str();
-		}
-		template<typename T, typename Elem, typename Traits>
-		inline SPROUT_NON_CONSTEXPR std::basic_istream<Elem, Traits>&
-		operator>>(std::basic_istream<Elem, Traits>& lhs, sprout::math::quaternion<T>& rhs) {
-			std::ctype<Elem> const& ct = std::use_facet<std::ctype<Elem> >(lhs.getloc());
-			T a = T();
-			T b = T();
-			T c = T();
-			T d = T();
-			sprout::complex<T> u = sprout::complex<T>();
-			sprout::complex<T> v = sprout::complex<T>();
-			Elem ch = Elem();
-			char cc;
-			lhs >> ch;
-			if (!lhs.good()) {
-				goto finish;
-			}
-			cc = ct.narrow(ch, char());
-			if (cc == '(') {
-				lhs >> ch;
-				if (!lhs.good()) {
-					goto finish;
-				}
-				cc = ct.narrow(ch, char());
-				if (cc == '(') {
-					lhs.putback(ch);
-					lhs >> u;
-					a = u.real();
-					b = u.imag();
-					if (!lhs.good()) {
-						goto finish;
-					}
-					lhs >> ch;
-					if (!lhs.good()) {
-						goto finish;
-					}
-					cc = ct.narrow(ch, char());
-					if (cc == ')') {
-						rhs = sprout::math::quaternion<T>(a, b);
-					} else if (cc == ',') {
-						lhs >> v;
-						c = v.real();
-						d = v.imag();
-						if (!lhs.good()) {
-							goto finish;
-						}
-						lhs >> ch;
-						if (!lhs.good()) {
-							goto finish;
-						}
-						cc = ct.narrow(ch, char());
-						if (cc == ')') {
-							rhs = sprout::math::quaternion<T>(a, b, c, d);
-						} else {
-							lhs.setstate(std::ios_base::failbit);
-						}
-					} else {
-						lhs.setstate(std::ios_base::failbit);
-					}
-				} else {
-					lhs.putback(ch);
-					lhs >> a;
-					if (!lhs.good()) {
-						goto finish;
-					}
-					lhs >> ch;
-					if (!lhs.good()) {
-						goto finish;
-					}
-					cc = ct.narrow(ch, char());
-					if (cc == ')') {
-						rhs = sprout::math::quaternion<T>(a);
-					} else if (cc == ',') {
-						lhs >> ch;
-						if (!lhs.good()) {
-							goto finish;
-						}
-						cc = ct.narrow(ch, char());
-						if (cc == '(') {
-							lhs.putback(ch);
-							lhs >> v;
-							c = v.real();
-							d = v.imag();
-							if (!lhs.good()) {
-								goto finish;
-							}
-							lhs >> ch;
-							if (!lhs.good()) {
-								goto finish;
-							}
-							cc = ct.narrow(ch, char());
-							if (cc == ')') {
-								rhs = sprout::math::quaternion<T>(a, b, c, d);
-							} else {
-								lhs.setstate(std::ios_base::failbit);
-							}
-						} else {
-							lhs.putback(ch);
-							lhs >> b;
-							if (!lhs.good()) {
-								goto finish;
-							}
-							lhs >> ch;
-							if (!lhs.good()) {
-								goto finish;
-							}
-							cc = ct.narrow(ch, char());
-							if (cc == ')') {
-								rhs = sprout::math::quaternion<T>(a, b);
-							} else if (cc == ',') {
-								lhs >> c;
-								if (!lhs.good()) {
-									goto finish;
-								}
-								lhs >> ch;
-								if (!lhs.good()) {
-									goto finish;
-								}
-								cc = ct.narrow(ch, char());
-								if (cc == ')') {
-									rhs = sprout::math::quaternion<T>(a, b, c);
-								} else if (cc == ',') {
-									lhs >> d;
-									if (!lhs.good()) {
-										goto finish;
-									}
-									lhs >> ch;
-									if (!lhs.good()) {
-										goto finish;
-									}
-									cc = ct.narrow(ch, char());
-									if (cc == ')') {
-										rhs = sprout::math::quaternion<T>(a, b, c, d);
-									} else {
-										lhs.setstate(std::ios_base::failbit);
-									}
-								} else {
-									lhs.setstate(std::ios_base::failbit);
-								}
-							} else {
-								lhs.setstate(std::ios_base::failbit);
-							}
-						}
-					} else {
-						lhs.setstate(std::ios_base::failbit);
-					}
-				}
-			} else {
-				lhs.putback(ch);
-				lhs >> a;
-				if (!lhs.good()) {
-					goto finish;
-				}
-				rhs = sprout::math::quaternion<T>(a);
-			}
-		finish:
-			return lhs;
-		}
-
-		//
-		// real
-		// unreal
-		//
-		template<typename T>
-		inline SPROUT_CONSTEXPR T
-		real(sprout::math::quaternion<T> const& q) {
-			return q.real();
-		}
-		template<typename T>
-		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-		unreal(sprout::math::quaternion<T> const& q) {
-			return q.unreal();
-		}
-
-		//
-		// sup
-		// l1
-		//
-		template<typename T>
-		inline SPROUT_CONSTEXPR T
-		sup(sprout::math::quaternion<T> const& q) {
-			return sprout::math::detail::abs_max(
-				sprout::array<T, 4>{{
-					q.R_component_1(),
-					q.R_component_2(),
-					q.R_component_3(),
-					q.R_component_4()
-					}}
-				);
-		}
-		template<typename T>
-		inline SPROUT_CONSTEXPR T
-		l1(sprout::math::quaternion<T> const& q) {
-			return sprout::math::detail::abs_sum(
-				sprout::array<T, 4>{{
-					q.R_component_1(),
-					q.R_component_2(),
-					q.R_component_3(),
-					q.R_component_4()
-					}}
-				);
-		}
-
-		//
-		// abs
-		//
-		namespace detail {
-			template<typename T>
-			inline SPROUT_CONSTEXPR T
-			abs_q_impl_3(sprout::array<T, 4> const& temp, T const& maxim) {
-				return maxim * sprout::math::sqrt(sprout::math::detail::sum(sprout::math::detail::mul(temp, temp)));
-			}
-			template<typename T>
-			inline SPROUT_CONSTEXPR T
-			abs_q_impl_2(sprout::array<T, 4> const& temp, T const& maxim) {
-				return sprout::math::detail::abs_q_impl_3(
-					sprout::math::detail::mul(temp, maxim), maxim
-					);
-			}
-			template<typename T>
-			inline SPROUT_CONSTEXPR T
-			abs_q_impl_1(sprout::array<T, 4> const& temp, T const& maxim) {
-				return maxim == static_cast<T>(0) ? sprout::math::quaternion<T>(maxim)
-					: sprout::math::detail::abs_q_impl_2(
-						temp, static_cast<T>(1) / maxim
-						)
-					;
-			}
-			template<typename T>
-			inline SPROUT_CONSTEXPR T
-			abs_q_impl(sprout::array<T, 4> const& temp) {
-				return sprout::math::detail::abs_q_impl_1(
-					temp, sprout::math::detail::abs_max(temp)
-					);
-			}
-		}	// namespace detail
-		template<typename T>
-		inline SPROUT_CONSTEXPR T
-		abs(sprout::math::quaternion<T> const& q) {
-			return sprout::math::detail::abs_q_impl(
-				sprout::array<T, 4>{{
-					q.R_component_1(),
-					q.R_component_2(),
-					q.R_component_3(),
-					q.R_component_4()
-					}}
-				);
-		}
-
-#undef	SPROUT_QUATERNION_ARRAY_LOADER
-
-		//
-		// conj
-		// norm
-		//
-		template<typename T>
-		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-		conj(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()
-				);
-		}
-		template<typename T>
-		inline SPROUT_CONSTEXPR T
-		norm(sprout::math::quaternion<T> const& q) {
-			return sprout::math::real(q * sprout::math::conj(q));
-		}
-
-		//
-		// spherical
-		// semipolar
-		// multipolar
-		// cylindrospherical
-		// cylindrical
-		//
-		namespace detail {
-			template<typename T>
-			inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-			spherical_impl(T const& rho, T const& theta, T const& phi1, T const& phi2, T const& p1, T const& p2) {
-				return rho * sprout::math::quaternion<T>(
-					sprout::math::cos(theta) * (p2 * p1),
-					sprout::math::sin(theta) * (p2 * p1),
-					sprout::math::sin(phi1) * p2,
-					sprout::math::sin(phi2)
-					);
-			}
-		}	// namespace detail
-		template<typename T>
-		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-		spherical(T const& rho, T const& theta, T const& phi1, T const& phi2) {
-			return sprout::math::detail::spherical_impl(
-				rho, theta, phi1, phi2,
-				sprout::math::cos(phi1), sprout::math::cos(phi2)
-				);
-		}
-		template<typename T>
-		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-		semipolar(T const& rho, T const& alpha, T const& theta1, T const& theta2) {
-			return rho * sprout::math::quaternion<T>(
-				sprout::math::cos(alpha) * sprout::math::cos(theta1),
-				sprout::math::cos(alpha) * sprout::math::sin(theta1),
-				sprout::math::sin(alpha) * sprout::math::cos(theta2),
-				sprout::math::sin(alpha) * sprout::math::sin(theta2)
-				);
-		}
-		template<typename T>
-		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-		multipolar(T const& rho1, T const& theta1, T const& rho2, T const& theta2) {
-			return sprout::math::quaternion<T>(
-				rho1 * sprout::math::cos(theta1),
-				rho1 * sprout::math::sin(theta1),
-				rho2 * sprout::math::cos(theta2),
-				rho2 * sprout::math::sin(theta2)
-				);
-		}
-		template<typename T>
-		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-		cylindrospherical(T const& t, T const& radius, T const& longitude, T const& latitude) {
-			return sprout::math::quaternion<T>(
-				t,
-				radius * sprout::math::cos(longitude) * sprout::math::cos(latitude),
-				radius * sprout::math::sin(longitude) * sprout::math::cos(latitude),
-				radius * sprout::math::sin(latitude)
-				);
-		}
-		template<typename T>
-		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-		cylindrical(T const& r, T const& angle, T const& h1, T const& h2) {
-			return sprout::math::quaternion<T>(
-				r * sprout::math::cos(angle),
-				r * sprout::math::sin(angle),
-				h1,
-				h2
-				);
-		}
-
-		//
-		// exp
-		//
-		// !!!
-//		namespace detail {
-//			template<typename T>
-//			inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-//			exp_impl_1(sprout::math::quaternion<T> const& q, T const& z, T const& w) {
-//				return sprout::math::exp(sprout::math::real(q)) * sprout::math::quaternion<T>(
-//					sprout::math::cos(z),
-//					w * q.R_component_2(),
-//					w * q.R_component_3(),
-//					w * q.R_component_4()
-//					);
-//			}
-//			template<typename T>
-//			inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-//			exp_impl(sprout::math::quaternion<T> const& q, T const& z) {
-//				return sprout::math::detail::exp_impl_1(
-//					q, z,
-//					sprout::math::sinc_pi(z)
-//					);
-//			}
-//		}	// namespace detail
-//		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-//		exp(sprout::math::quaternion<T> const& q) {
-//			return sprout::math::detail::exp_impl(
-//				q,
-//				sprout::math::abs(sprout::math::unreal(q))
-//				);
-//		}
-
-		//
-		// cos
-		// sin
-		// tan
-		//
-		// !!!
-//		namespace detail {
-//			template<typename T>
-//			inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-//			cos_impl_1(sprout::math::quaternion<T> const& q, T const& z, T const& w) {
-//				return sprout::math::quaternion<T>(
-//					sprout::math::cos(q.real()) * sprout::math::cosh(z),
-//					w * q.R_component_2(),
-//					w * q.R_component_3(),
-//					w * q.R_component_4()
-//					);
-//			}
-//			template<typename T>
-//			inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-//			cos_impl(sprout::math::quaternion<T> const& q, T const& z) {
-//				return sprout::math::detail::cos_impl_1(
-//					q, z,
-//					-sprout::math::sin(q.real()) * sprout::math::sinhc_pi(z)
-//					);
-//			}
-//		}	// namespace detail
-//		template<typename T>
-//		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-//		cos(sprout::math::quaternion<T> const& q) {
-//			return sprout::math::detail::cos_impl(
-//				q,
-//				sprout::math::abs(sprout::math::unreal(q))
-//				);
-//		}
-//		namespace detail {
-//			template<typename T>
-//			inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-//			sin_impl_1(sprout::math::quaternion<T> const& q, T const& z, T const& w) {
-//				return sprout::math::quaternion<T>(
-//					sprout::math::sin(q.real()) * sprout::math::cosh(z),
-//					w * q.R_component_2(),
-//					w * q.R_component_3(),
-//					w * q.R_component_4()
-//					);
-//			}
-//			template<typename T>
-//			inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-//			sin_impl(sprout::math::quaternion<T> const& q, T const& z) {
-//				return sprout::math::detail::sin_impl_1(
-//					q, z,
-//					+sprout::math::cos(q.real()) * sprout::math::sinhc_pi(z)
-//					);
-//			}
-//		}	// namespace detail
-//		template<typename T>
-//		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-//		sin(sprout::math::quaternion<T> const& q) {
-//			return sprout::math::detail::sin_impl(
-//				q,
-//				sprout::math::abs(sprout::math::unreal(q))
-//				);
-//		}
-//		template<typename T>
-//		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-//		tan(sprout::math::quaternion<T> const& q) {
-//			return sprout::math::sin(q) / sprout::math::cos(q);
-//		}
-
-		//
-		// cosh
-		// sinh
-		// tanh
-		//
-		// !!!
-//		template<typename T>
-//		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-//		cosh(sprout::math::quaternion<T> const& q) {
-//			return (sprout::math::exp(+q) + sprout::math::exp(-q)) / static_cast<T>(2);
-//		}
-//		template<typename T>
-//		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-//		sinh(sprout::math::quaternion<T> const& q) {
-//			return (sprout::math::exp(+q) - sprout::math::exp(-q)) / static_cast<T>(2);
-//		}
-//		template<typename T>
-//		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-//		tanh(sprout::math::quaternion<T> const& q) {
-//			return sprout::math::sinh(q) / sprout::math::cosh(q);
-//		}
-
-		//
-		// pow
-		//
-		namespace detail {
-			template<typename T>
-			inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-			pow_q_impl(sprout::math::quaternion<T> const& q, int n, int	m, sprout::math::quaternion<T> const& result) {
-				return n != m << 1 ? result * result * q
-					: result * result
-					;
-			}
-		}	// namespace detail
-		template<typename T>
-		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
-		pow(sprout::math::quaternion<T> const& q, int n) {
-			return n > 1 ? sprout::math::detail::pow_q_impl(
-					q, n, n >> 1, sprout::math::pow(q, n >> 1)
-					)
-				: n == 1 ? q
-				: n == 0 ? sprout::math::quaternion<T>(static_cast<T>(1))
-				: sprout::math::pow(sprout::math::quaternion<T>(static_cast<T>(1)) / q, -n)
-				;
-		}
-	}	// namespace math
-
-	using sprout::math::quaternion;
-	using sprout::math::real;
-	using sprout::math::unreal;
-	using sprout::math::sup;
-	using sprout::math::l1;
-	using sprout::math::abs;
-	using sprout::math::conj;
-	using sprout::math::norm;
-	using sprout::math::spherical;
-	using sprout::math::semipolar;
-	using sprout::math::multipolar;
-	using sprout::math::cylindrospherical;
-	using sprout::math::cylindrical;
-//	using sprout::math::exp;
-//	using sprout::math::cos;
-//	using sprout::math::sin;
-//	using sprout::math::tan;
-//	using sprout::math::cosh;
-//	using sprout::math::sinh;
-//	using sprout::math::tanh;
-	using sprout::math::pow;
-}	// namespace sprout
+#include <sprout/math/quaternion/quaternion.hpp>
+#include <sprout/math/quaternion/container.hpp>
 
 #endif	// #ifndef SPROUT_MATH_QUATERNION_HPP
diff --git a/sprout/math/quaternion/container.hpp b/sprout/math/quaternion/container.hpp
new file mode 100644
index 00000000..9f66d093
--- /dev/null
+++ b/sprout/math/quaternion/container.hpp
@@ -0,0 +1,43 @@
+/*=============================================================================
+  Copyright (c) 2011-2016 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_QUATERNION_CONTAINER_HPP
+#define SPROUT_QUATERNION_CONTAINER_HPP
+
+#include <type_traits>
+#include <sprout/utility/forward.hpp>
+#include <sprout/math/quaternion/quaternion.hpp>
+#include <sprout/container/traits.hpp>
+
+namespace sprout {
+	//
+	// container_construct_traits
+	//
+	template<typename T>
+	struct container_construct_traits<sprout::math::quaternion<T> > {
+	public:
+		typedef sprout::math::quaternion<T> copied_type;
+	public:
+		template<typename Cont>
+		static SPROUT_CONSTEXPR copied_type
+		deep_copy(Cont&& cont) {
+			return SPROUT_FORWARD(Cont, cont);
+		}
+		template<typename... Args>
+		static SPROUT_CONSTEXPR copied_type
+		make(Args&&... args) {
+			return copied_type(SPROUT_FORWARD(Args, args)...);
+		}
+		template<typename Cont, typename... Args>
+		static SPROUT_CONSTEXPR copied_type
+		remake(Cont&&, typename sprout::container_traits<sprout::math::quaternion<T> >::difference_type, Args&&... args) {
+			return copied_type(SPROUT_FORWARD(Args, args)...);
+		}
+	};
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_QUATERNION_CONTAINER_HPP
diff --git a/sprout/math/quaternion/quaternion.hpp b/sprout/math/quaternion/quaternion.hpp
new file mode 100644
index 00000000..6cd10073
--- /dev/null
+++ b/sprout/math/quaternion/quaternion.hpp
@@ -0,0 +1,1734 @@
+/*=============================================================================
+  Copyright (c) 2011-2016 Bolero MURAKAMI
+  https://github.com/bolero-MURAKAMI/Sprout
+
+  Distributed under the sprout Software License, Version 1.0. (See accompanying
+  file LICENSE_1_0.txt or copy at http://www.sprout.org/LICENSE_1_0.txt)
+=============================================================================*/
+#ifndef SPROUT_MATH_QUATERNION_QUATERNION_HPP
+#define SPROUT_MATH_QUATERNION_QUATERNION_HPP
+
+#include <iosfwd>
+#include <sstream>
+#include <locale>
+#include <sprout/config.hpp>
+#include <sprout/array/array.hpp>
+#include <sprout/math/abs.hpp>
+#include <sprout/math/cos.hpp>
+#include <sprout/math/sin.hpp>
+#include <sprout/math/cosh.hpp>
+#include <sprout/math/exp.hpp>
+#include <sprout/math/abs.hpp>
+//#include <sprout/math/sinc.hpp>
+//#include <sprout/math/sinhc.hpp>
+#include <sprout/complex/complex.hpp>
+#include <sprout/range/algorithm/max_element.hpp>
+#include <sprout/range/numeric/accumulate.hpp>
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+			template<typename T>
+			class abs_less {
+			public:
+				SPROUT_CONSTEXPR T
+				operator()(T const& lhs, T const& rhs) const {
+					return sprout::math::abs(lhs) < sprout::math::abs(rhs);
+				}
+			};
+			template<typename T>
+			class abs_plus {
+			public:
+				SPROUT_CONSTEXPR T
+				operator()(T const& lhs, T const& rhs) const {
+					return sprout::math::abs(lhs) + sprout::math::abs(rhs);
+				}
+			};
+			template<typename T, std::size_t N>
+			SPROUT_CONSTEXPR T
+			abs_max(sprout::array<T, N> const& c) {
+				return sprout::math::abs(*sprout::range::max_element(c, sprout::math::detail::abs_less<T>()));
+			}
+			template<typename T, std::size_t N>
+			SPROUT_CONSTEXPR T
+			sum(sprout::array<T, N> const& c) {
+				return sprout::range::accumulate(c, static_cast<T>(0));
+			}
+			template<typename T, std::size_t N>
+			SPROUT_CONSTEXPR T
+			abs_sum(sprout::array<T, N> const& c) {
+				return sprout::range::accumulate(c, static_cast<T>(0), sprout::math::detail::abs_plus<T>());
+			}
+			template<typename T>
+			SPROUT_CONSTEXPR sprout::array<T, 2>
+			mul(sprout::array<T, 2> const& l, T const& r) {
+				return sprout::array<T, 2>{{
+					l[0] * r,
+					l[1] * r,
+					}};
+			}
+			template<typename T>
+			SPROUT_CONSTEXPR sprout::array<T, 2>
+			mul(sprout::array<T, 2> const& l, sprout::array<T, 2> const& r) {
+				return sprout::array<T, 2>{{
+					l[0] * r[0],
+					l[1] * r[1],
+					}};
+			}
+			template<typename T>
+			SPROUT_CONSTEXPR sprout::array<T, 4>
+			mul(sprout::array<T, 4> const& l, T const& r) {
+				return sprout::array<T, 4>{{
+					l[0] * r,
+					l[1] * r,
+					l[2] * r,
+					l[3] * r
+					}};
+			}
+			template<typename T>
+			SPROUT_CONSTEXPR sprout::array<T, 4>
+			mul(sprout::array<T, 4> const& l, sprout::array<T, 4> const& r) {
+				return sprout::array<T, 4>{{
+					l[0] * r[0],
+					l[1] * r[1],
+					l[2] * r[2],
+					l[3] * r[3]
+					}};
+			}
+		}	// namespace detail
+
+#define	SPROUT_QUATERNION_ACCESSOR_GENERATOR(type) \
+			SPROUT_CONSTEXPR type real() const { \
+				return (elems_[0]); \
+			} \
+			SPROUT_CONSTEXPR quaternion<type> unreal() const { \
+				return (quaternion<type>(static_cast<type>(0), elems_[1], elems_[2], elems_[3])); \
+			} \
+			SPROUT_CONSTEXPR type R_component_1() const { \
+				return (elems_[0]); \
+			} \
+			SPROUT_CONSTEXPR type R_component_2() const { \
+				return (elems_[1]); \
+			} \
+			SPROUT_CONSTEXPR type R_component_3() const { \
+				return (elems_[2]); \
+			} \
+			SPROUT_CONSTEXPR type R_component_4() const { \
+				return (elems_[3]); \
+			} \
+			SPROUT_CONSTEXPR sprout::complex<type> C_component_1() const { \
+				return sprout::complex<type>(elems_[0], elems_[1]); \
+			} \
+			SPROUT_CONSTEXPR sprout::complex<type> C_component_2() const { \
+				return sprout::complex<type>(elems_[2], elems_[3]); \
+			}
+
+#define	SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(type) \
+			template<typename X> \
+			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator=(quaternion<X> const& a_affecter) { \
+				elems_[0] = static_cast<type>(a_affecter.R_component_1()); \
+				elems_[1] = static_cast<type>(a_affecter.R_component_2()); \
+				elems_[2] = static_cast<type>(a_affecter.R_component_3()); \
+				elems_[3] = static_cast<type>(a_affecter.R_component_4()); \
+				return *this; \
+			} \
+			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator=(quaternion<type> const& a_affecter) { \
+				elems_[0] = a_affecter.elems_[0]; \
+				elems_[1] = a_affecter.elems_[1]; \
+				elems_[2] = a_affecter.elems_[2]; \
+				elems_[3] = a_affecter.elems_[3]; \
+				return *this; \
+			} \
+			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator=(type const& a_affecter) { \
+				elems_[0] = a_affecter; \
+				elems_[1] = elems_[2] = elems_[3] = static_cast<type>(0); \
+				return *this; \
+			} \
+			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator=(sprout::complex<type> const& a_affecter) { \
+				elems_[0] = a_affecter.real(); \
+				elems_[1] = a_affecter.imag(); \
+				elems_[2] = elems_[3] = static_cast<type>(0); \
+				return *this; \
+			}
+
+		//
+		// quaternion
+		//
+		template<typename T>
+		class quaternion {
+		private:
+			typedef sprout::array<T, 4> array_type;
+		public:
+			typedef T value_type;
+			typedef typename array_type::iterator iterator;
+			typedef typename array_type::const_iterator const_iterator;
+			typedef typename array_type::reference reference;
+			typedef typename array_type::const_reference const_reference;
+			typedef typename array_type::size_type size_type;
+			typedef typename array_type::pointer pointer;
+			typedef typename array_type::const_pointer const_pointer;
+			typedef typename array_type::reverse_iterator reverse_iterator;
+			typedef typename array_type::const_reverse_iterator const_reverse_iterator;
+		public:
+			SPROUT_STATIC_CONSTEXPR size_type static_size = array_type::static_size;
+		private:
+			array_type elems_;
+		public:
+			explicit SPROUT_CONSTEXPR quaternion(
+				T const& requested_a = T(),
+				T const& requested_b = T(),
+				T const& requested_c = T(),
+				T const& requested_d = T()
+				)
+				: elems_{{requested_a, requested_b, requested_c, requested_d}}
+			{}
+			explicit SPROUT_CONSTEXPR quaternion(
+				sprout::complex<T> const& z0,
+				sprout::complex<T> const& z1 = sprout::complex<T>()
+				)
+				: elems_{{z0.real(), z0.imag(), z1.real(), z1.imag()}}
+			{}
+			template<typename X>
+			explicit SPROUT_CONSTEXPR quaternion(quaternion<X> const& a_recopier)
+				: elems_{{
+					static_cast<T>(a_recopier.R_component_1()),
+					static_cast<T>(a_recopier.R_component_2()),
+					static_cast<T>(a_recopier.R_component_3()),
+					static_cast<T>(a_recopier.R_component_4())
+					}}
+			{}
+			SPROUT_QUATERNION_ACCESSOR_GENERATOR(T)
+			SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(T)
+			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator+=(T const& rhs) {
+				T at = elems_[0] + rhs;
+				elems_[0] = at;
+				return *this;
+			}
+			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator+=(sprout::complex<T> const& rhs) {
+				T at = elems_[0] + rhs.real();
+				T bt = elems_[1] + rhs.imag();
+				elems_[0] = at; 
+				elems_[1] = bt;
+				return *this;
+			}
+			template<typename X>
+			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator+=(quaternion<X> const& rhs) {
+				T at = elems_[0] + static_cast<T>(rhs.R_component_1());
+				T bt = elems_[1] + static_cast<T>(rhs.R_component_2());
+				T ct = elems_[2] + static_cast<T>(rhs.R_component_3());
+				T dt = elems_[3] + static_cast<T>(rhs.R_component_4());
+				elems_[0] = at;
+				elems_[1] = bt;
+				elems_[2] = ct;
+				elems_[3] = dt;
+				return *this;
+			}
+			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator-=(T const& rhs) {
+				T at = elems_[0] - rhs;
+				elems_[0] = at;
+				return *this;
+			}
+			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator-=(sprout::complex<T> const& rhs) {
+				T at = elems_[0] - rhs.real();
+				T bt = elems_[1] - rhs.imag();
+				elems_[0] = at;
+				elems_[1] = bt;
+				return *this;
+			}
+			template<typename X>
+			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator-=(quaternion<X> const& rhs) {
+				T at = elems_[0] - static_cast<T>(rhs.R_component_1());
+				T bt = elems_[1] - static_cast<T>(rhs.R_component_2());
+				T ct = elems_[2] - static_cast<T>(rhs.R_component_3());
+				T dt = elems_[3] - static_cast<T>(rhs.R_component_4());
+				elems_[0] = at;
+				elems_[1] = bt;
+				elems_[2] = ct;
+				elems_[3] = dt;
+				return *this;
+			}
+			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator*=(T const& rhs) {
+				T at = elems_[0] * rhs;
+				T bt = elems_[1] * rhs;
+				T ct = elems_[2] * rhs;
+				T dt = elems_[3] * rhs;
+				elems_[0] = at;
+				elems_[1] = bt;
+				elems_[2] = ct;
+				elems_[3] = dt;
+				return *this;
+			}
+			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator*=(sprout::complex<T> const& rhs) {
+				T ar = rhs.real();
+				T br = rhs.imag();
+				T at = +elems_[0] * ar - elems_[1] * br;
+				T bt = +elems_[0] * br + elems_[1] * ar;
+				T ct = +elems_[2] * ar + elems_[3] * br;
+				T dt = -elems_[2] * br + elems_[3] * ar;
+				elems_[0] = at;
+				elems_[1] = bt;
+				elems_[2] = ct;
+				elems_[3] = dt;
+				return *this;
+			}
+			template<typename X>
+			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator*=(quaternion<X> const& rhs) {
+				T ar = static_cast<T>(rhs.R_component_1());
+				T br = static_cast<T>(rhs.R_component_2());
+				T cr = static_cast<T>(rhs.R_component_3());
+				T dr = static_cast<T>(rhs.R_component_4());
+				T at = +elems_[0] * ar - elems_[1] * br - elems_[2] * cr - elems_[3] * dr;
+				T bt = +elems_[0] * br + elems_[1] * ar + elems_[2] * dr - elems_[3] * cr;
+				T ct = +elems_[0] * cr - elems_[1] * dr + elems_[2] * ar + elems_[3] * br;
+				T dt = +elems_[0] * dr + elems_[1] * cr - elems_[2] * br + elems_[3] * ar;
+				elems_[0] = at;
+				elems_[1] = bt;
+				elems_[2] = ct;
+				elems_[3] = dt;
+				return *this;
+			}
+			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator/=(T const& rhs) {
+				T at = elems_[0] / rhs;
+				T bt = elems_[1] / rhs;
+				T ct = elems_[2] / rhs;
+				T dt = elems_[3] / rhs;
+				elems_[0] = at;
+				elems_[1] = bt;
+				elems_[2] = ct;
+				elems_[3] = dt;
+				return *this;
+			}
+			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator/=(sprout::complex<T> const& rhs) {
+				T ar = rhs.real();
+				T br = rhs.imag();
+				T denominator = ar * ar + br * br;
+				T at =(+elems_[0] * ar + elems_[1] * br) / denominator;
+				T bt =(-elems_[0] * br + elems_[1] * ar) / denominator;
+				T ct =(+elems_[2] * ar - elems_[3] * br) / denominator;
+				T dt =(+elems_[2] * br + elems_[3] * ar) / denominator;
+				elems_[0] = at;
+				elems_[1] = bt;
+				elems_[2] = ct;
+				elems_[3] = dt;
+				return *this;
+			}
+			template<typename X>
+			SPROUT_CXX14_CONSTEXPR quaternion<T>& operator/=(quaternion<X> const& rhs) {
+				T ar = static_cast<T>(rhs.R_component_1());
+				T br = static_cast<T>(rhs.R_component_2());
+				T cr = static_cast<T>(rhs.R_component_3());
+				T dr = static_cast<T>(rhs.R_component_4());
+				T denominator = ar * ar + br * br + cr * cr + dr * dr;
+				T at =(+elems_[0] * ar + elems_[1] * br + elems_[2] * cr + elems_[3] * dr) / denominator;
+				T bt =(-elems_[0] * br + elems_[1] * ar - elems_[2] * dr + elems_[3] * cr) / denominator;
+				T ct =(-elems_[0] * cr + elems_[1] * dr + elems_[2] * ar - elems_[3] * br) / denominator;
+				T dt =(-elems_[0] * dr - elems_[1] * cr + elems_[2] * br + elems_[3] * ar) / denominator;
+				elems_[0] = at;
+				elems_[1] = bt;
+				elems_[2] = ct;
+				elems_[3] = dt;
+				return *this;
+			}
+			// iterators:
+			SPROUT_CXX14_CONSTEXPR iterator begin() SPROUT_NOEXCEPT {
+				return elems_.begin();
+			}
+			SPROUT_CONSTEXPR const_iterator begin() const SPROUT_NOEXCEPT {
+				return elems_.begin();
+			}
+			SPROUT_CXX14_CONSTEXPR iterator end() SPROUT_NOEXCEPT {
+				return elems_.end();
+			}
+			SPROUT_CONSTEXPR const_iterator end() const SPROUT_NOEXCEPT {
+				return elems_.end();
+			}
+			SPROUT_CXX14_CONSTEXPR reverse_iterator rbegin() SPROUT_NOEXCEPT {
+				return elems_.rbegin();
+			}
+			SPROUT_CONSTEXPR const_reverse_iterator rbegin() const SPROUT_NOEXCEPT {
+				return elems_.rbegin();
+			}
+			SPROUT_CXX14_CONSTEXPR reverse_iterator rend() SPROUT_NOEXCEPT {
+				return elems_.rend();
+			}
+			SPROUT_CONSTEXPR const_reverse_iterator rend() const SPROUT_NOEXCEPT {
+				return elems_.rend();
+			}
+			SPROUT_CONSTEXPR const_iterator cbegin() const SPROUT_NOEXCEPT {
+				return elems_.cbegin();
+			}
+			SPROUT_CONSTEXPR const_iterator cend() const SPROUT_NOEXCEPT {
+				return elems_.cbegin();
+			}
+			SPROUT_CONSTEXPR const_reverse_iterator crbegin() const SPROUT_NOEXCEPT {
+				return elems_.crbegin();
+			}
+			SPROUT_CONSTEXPR const_reverse_iterator crend() const SPROUT_NOEXCEPT {
+				return elems_.crend();
+			}
+			// capacity:
+			SPROUT_CONSTEXPR size_type size() const SPROUT_NOEXCEPT {
+				return elems_.size();
+			}
+			SPROUT_CONSTEXPR size_type max_size() const SPROUT_NOEXCEPT {
+				return elems_.max_size();
+			}
+			SPROUT_CONSTEXPR bool empty() const SPROUT_NOEXCEPT {
+				return elems_.empty();
+			}
+			// element access:
+			SPROUT_CXX14_CONSTEXPR reference operator[](size_type i) {
+				return elems_[i];
+			}
+			SPROUT_CONSTEXPR const_reference operator[](size_type i) const {
+				return elems_[i];
+			}
+			SPROUT_CXX14_CONSTEXPR reference at(size_type i) {
+				return elems_.at(i);
+			}
+			SPROUT_CONSTEXPR const_reference at(size_type i) const {
+				return elems_.at(i);
+			}
+			SPROUT_CXX14_CONSTEXPR reference front() {
+				return elems_.front();
+			}
+			SPROUT_CONSTEXPR const_reference front() const {
+				return elems_.front();
+			}
+			SPROUT_CXX14_CONSTEXPR reference back() {
+				return elems_.back();
+			}
+			SPROUT_CONSTEXPR const_reference back() const {
+				return elems_.back();
+			}
+
+			SPROUT_CXX14_CONSTEXPR pointer data() SPROUT_NOEXCEPT {
+				return elems_.data();
+			}
+			SPROUT_CONSTEXPR const_pointer data() const SPROUT_NOEXCEPT {
+				return elems_.data();
+			}
+			SPROUT_CXX14_CONSTEXPR pointer c_array() SPROUT_NOEXCEPT {
+				return elems_.c_array();
+			}
+			SPROUT_CONSTEXPR const_pointer c_array() const SPROUT_NOEXCEPT {
+				return elems_.c_array();
+			}
+		};
+		template<typename T>
+		SPROUT_CONSTEXPR_OR_CONST typename sprout::math::quaternion<T>::size_type sprout::math::quaternion<T>::static_size;
+
+		template<>
+		class quaternion<float>;
+		template<>
+		class quaternion<double>;
+		template<>
+		class quaternion<long double>;
+
+#define	SPROUT_QUATERNION_MEMBER_TYPE_DATA_GENERATOR(type) \
+		private: \
+			typedef sprout::array<type, 4> array_type; \
+		public: \
+			typedef type value_type; \
+			typedef typename array_type::iterator iterator; \
+			typedef typename array_type::const_iterator const_iterator; \
+			typedef typename array_type::reference reference; \
+			typedef typename array_type::const_reference const_reference; \
+			typedef typename array_type::size_type size_type; \
+			typedef typename array_type::pointer pointer; \
+			typedef typename array_type::const_pointer const_pointer; \
+			typedef typename array_type::reverse_iterator reverse_iterator; \
+			typedef typename array_type::const_reverse_iterator const_reverse_iterator; \
+		public: \
+			SPROUT_STATIC_CONSTEXPR size_type static_size = array_type::static_size; \
+		private: \
+			array_type elems_;
+
+#define	SPROUT_QUATERNION_CONSTRUCTOR_GENERATOR(type) \
+			explicit SPROUT_CONSTEXPR quaternion( \
+				type const& requested_a = static_cast<type>(0), \
+				type const& requested_b = static_cast<type>(0), \
+				type const& requested_c = static_cast<type>(0), \
+				type const& requested_d = static_cast<type>(0) \
+				) \
+				: elems_{{requested_a, requested_a, requested_c, requested_d}} \
+			{} \
+			explicit SPROUT_CONSTEXPR quaternion( \
+				sprout::complex<type> const& z0, \
+				sprout::complex<type> const& z1 = sprout::complex<type>() \
+				) \
+				: elems_{{z0.real(), z0.imag(), z1.real(), z1.imag()}} \
+			{}
+
+#define	SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_1(type) \
+			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator+=(type const& rhs) { \
+				elems_[0] += rhs; \
+				return *this; \
+			}
+
+#define	SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_2(type) \
+			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator+=(sprout::complex<type> const& rhs) { \
+				elems_[0] += rhs.real(); \
+				elems_[1] += rhs.imag(); \
+				return *this; \
+			}
+
+#define	SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_3(type) \
+			template<typename X> \
+			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator+=(quaternion<X> const& rhs) { \
+				elems_[0] += static_cast<type>(rhs.R_component_1()); \
+				elems_[1] += static_cast<type>(rhs.R_component_2()); \
+				elems_[2] += static_cast<type>(rhs.R_component_3()); \
+				elems_[3] += static_cast<type>(rhs.R_component_4()); \
+				return *this; \
+			}
+
+#define	SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_1(type) \
+			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator-=(type const& rhs) { \
+				elems_[0] -= rhs; \
+				return *this; \
+			}
+
+#define	SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_2(type) \
+			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator-=(sprout::complex<type> const& rhs) { \
+				elems_[0] -= rhs.real(); \
+				elems_[1] -= rhs.imag(); \
+				return *this; \
+			}
+
+#define	SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_3(type) \
+			template<typename X> \
+			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator-=(quaternion<X> const& rhs) { \
+				elems_[0] -= static_cast<type>(rhs.R_component_1()); \
+				elems_[1] -= static_cast<type>(rhs.R_component_2()); \
+				elems_[2] -= static_cast<type>(rhs.R_component_3()); \
+				elems_[3] -= static_cast<type>(rhs.R_component_4()); \
+				return *this; \
+			}
+
+#define	SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_1(type) \
+			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator*=(type const& rhs) { \
+				elems_[0] *= rhs; \
+				elems_[1] *= rhs; \
+				elems_[2] *= rhs; \
+				elems_[3] *= rhs; \
+				return *this; \
+			}
+
+#define	SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_2(type) \
+			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator*=(sprout::complex<type> const& rhs) { \
+				type ar = rhs.real(); \
+				type br = rhs.imag(); \
+				type at = +elems_[0] * ar - elems_[1] * br; \
+				type bt = +elems_[0] * br + elems_[1] * ar; \
+				type ct = +elems_[2] * ar + elems_[3] * br; \
+				type dt = -elems_[2] * br + elems_[3] * ar; \
+				elems_[0] = at; \
+				elems_[1] = bt; \
+				elems_[2] = ct; \
+				elems_[3] = dt; \
+				return *this; \
+			}
+
+#define	SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_3(type) \
+			template<typename X> \
+			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator*=(quaternion<X> const& rhs) { \
+				type ar = static_cast<type>(rhs.R_component_1()); \
+				type br = static_cast<type>(rhs.R_component_2()); \
+				type cr = static_cast<type>(rhs.R_component_3()); \
+				type dr = static_cast<type>(rhs.R_component_4()); \
+				type at = +elems_[0] * ar - elems_[1] * br - elems_[2] * cr - elems_[3] * dr; \
+				type bt = +elems_[0] * br + elems_[1] * ar + elems_[2] * dr - elems_[3] * cr; \
+				type ct = +elems_[0] * cr - elems_[1] * dr + elems_[2] * ar + elems_[3] * br; \
+				type dt = +elems_[0] * dr + elems_[1] * cr - elems_[2] * br + elems_[3] * ar; \
+				elems_[0] = at; \
+				elems_[1] = bt; \
+				elems_[2] = ct; \
+				elems_[3] = dt; \
+				return *this; \
+			}
+
+#define	SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_1(type) \
+			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator/=(type const& rhs) { \
+				elems_[0] /= rhs; \
+				elems_[1] /= rhs; \
+				elems_[2] /= rhs; \
+				elems_[3] /= rhs; \
+				return *this; \
+			}
+
+#define	SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \
+			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator/=(sprout::complex<type> const& rhs) { \
+				sprout::array<type, 2> tr{{ \
+					rhs.real(), \
+					rhs.imag() \
+				}}; \
+				type mixam = static_cast<type>(1) / sprout::math::detail::abs_max(tr); \
+				tr = sprout::math::detail::mul(tr, mixam); \
+				sprout::array<type, 4> tt{{ \
+					+elems_[0] * tr[0] + elems_[1] * tr[1], \
+					-elems_[0] * tr[1] + elems_[1] * tr[0], \
+					+elems_[2] * tr[0] - elems_[3] * tr[1], \
+					+elems_[2] * tr[1] + elems_[3] * tr[0] \
+				}}; \
+				tr = sprout::math::detail::mul(tr, tr); \
+				tt = sprout::math::detail::mul(tt, mixam / sprout::math::detail::sum(tr)); \
+				elems_[0] = tt[0]; \
+				elems_[1] = tt[1]; \
+				elems_[2] = tt[2]; \
+				elems_[3] = tt[3]; \
+				return *this; \
+			}
+
+#define	SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_3(type) \
+			template<typename X> \
+			SPROUT_CXX14_CONSTEXPR quaternion<type>& operator/=(quaternion<X> const& rhs) { \
+				sprout::array<type, 4> tr{{ \
+					static_cast<type>(rhs.R_component_1()), \
+					static_cast<type>(rhs.R_component_2()), \
+					static_cast<type>(rhs.R_component_3()), \
+					static_cast<type>(rhs.R_component_4()) \
+				}}; \
+				type mixam = static_cast<type>(1) / sprout::math::detail::abs_max(tr); \
+				tr = sprout::math::detail::mul(tr, mixam); \
+				sprout::array<type, 4> tt{{ \
+					+elems_[0] * tr[0] + elems_[1] * tr[1] + elems_[2] * tr[2] + elems_[3] * tr[3], \
+					-elems_[0] * tr[1] + elems_[1] * tr[0] - elems_[2] * tr[3] + elems_[3] * tr[2], \
+					-elems_[0] * tr[2] + elems_[1] * tr[3] + elems_[2] * tr[0] - elems_[3] * tr[1], \
+					-elems_[0] * tr[3] - elems_[1] * tr[2] + elems_[2] * tr[1] + elems_[3] * tr[0] \
+				}}; \
+				tr = sprout::math::detail::mul(tr, tr); \
+				tt = sprout::math::detail::mul(tt, mixam / sprout::math::detail::sum(tr)); \
+				elems_[0] = tt[0]; \
+				elems_[1] = tt[1]; \
+				elems_[2] = tt[2]; \
+				elems_[3] = tt[3]; \
+				return *this; \
+			}
+
+#define	SPROUT_QUATERNION_MEMBER_ADD_GENERATOR(type) \
+			SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_1(type) \
+			SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_2(type) \
+			SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_3(type)
+
+#define	SPROUT_QUATERNION_MEMBER_SUB_GENERATOR(type) \
+			SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_1(type) \
+			SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_2(type) \
+			SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_3(type)
+
+#define	SPROUT_QUATERNION_MEMBER_MUL_GENERATOR(type) \
+			SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_1(type) \
+			SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_2(type) \
+			SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_3(type)
+
+#define	SPROUT_QUATERNION_MEMBER_DIV_GENERATOR(type) \
+			SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_1(type) \
+			SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \
+			SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_3(type)
+
+#define	SPROUT_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(type) \
+			SPROUT_QUATERNION_MEMBER_ADD_GENERATOR(type) \
+			SPROUT_QUATERNION_MEMBER_SUB_GENERATOR(type) \
+			SPROUT_QUATERNION_MEMBER_MUL_GENERATOR(type) \
+			SPROUT_QUATERNION_MEMBER_DIV_GENERATOR(type)
+
+#define	SPROUT_QUATERNION_MEMBER_CONTAINER_GENERATOR(type) \
+			SPROUT_CXX14_CONSTEXPR iterator begin() SPROUT_NOEXCEPT { \
+				return elems_.begin(); \
+			} \
+			SPROUT_CONSTEXPR const_iterator begin() const SPROUT_NOEXCEPT { \
+				return elems_.begin(); \
+			} \
+			SPROUT_CXX14_CONSTEXPR iterator end() SPROUT_NOEXCEPT { \
+				return elems_.end(); \
+			} \
+			SPROUT_CONSTEXPR const_iterator end() const SPROUT_NOEXCEPT { \
+				return elems_.end(); \
+			} \
+			SPROUT_CXX14_CONSTEXPR reverse_iterator rbegin() SPROUT_NOEXCEPT { \
+				return elems_.rbegin(); \
+			} \
+			SPROUT_CONSTEXPR const_reverse_iterator rbegin() const SPROUT_NOEXCEPT { \
+				return elems_.rbegin(); \
+			} \
+			SPROUT_CXX14_CONSTEXPR reverse_iterator rend() SPROUT_NOEXCEPT { \
+				return elems_.rend(); \
+			} \
+			SPROUT_CONSTEXPR const_reverse_iterator rend() const SPROUT_NOEXCEPT { \
+				return elems_.rend(); \
+			} \
+			SPROUT_CONSTEXPR const_iterator cbegin() const SPROUT_NOEXCEPT { \
+				return elems_.cbegin(); \
+			} \
+			SPROUT_CONSTEXPR const_iterator cend() const SPROUT_NOEXCEPT { \
+				return elems_.cbegin(); \
+			} \
+			SPROUT_CONSTEXPR const_reverse_iterator crbegin() const SPROUT_NOEXCEPT { \
+				return elems_.crbegin(); \
+			} \
+			SPROUT_CONSTEXPR const_reverse_iterator crend() const SPROUT_NOEXCEPT { \
+				return elems_.crend(); \
+			} \
+			 \
+			SPROUT_CONSTEXPR size_type size() const SPROUT_NOEXCEPT { \
+				return elems_.size(); \
+			} \
+			SPROUT_CONSTEXPR size_type max_size() const SPROUT_NOEXCEPT { \
+				return elems_.max_size(); \
+			} \
+			SPROUT_CONSTEXPR bool empty() const SPROUT_NOEXCEPT { \
+				return elems_.empty(); \
+			} \
+			 \
+			SPROUT_CXX14_CONSTEXPR reference operator[](size_type i) { \
+				return elems_[i]; \
+			} \
+			SPROUT_CONSTEXPR const_reference operator[](size_type i) const { \
+				return elems_[i]; \
+			} \
+			SPROUT_CXX14_CONSTEXPR reference at(size_type i) { \
+				return elems_.at(i); \
+			} \
+			SPROUT_CONSTEXPR const_reference at(size_type i) const { \
+				return elems_.at(i); \
+			} \
+			SPROUT_CXX14_CONSTEXPR reference front() { \
+				return elems_.front(); \
+			} \
+			SPROUT_CONSTEXPR const_reference front() const { \
+				return elems_.front(); \
+			} \
+			SPROUT_CXX14_CONSTEXPR reference back() { \
+				return elems_.back(); \
+			} \
+			SPROUT_CONSTEXPR const_reference back() const { \
+				return elems_.back(); \
+			} \
+			 \
+			SPROUT_CXX14_CONSTEXPR pointer data() SPROUT_NOEXCEPT { \
+				return elems_.data(); \
+			} \
+			SPROUT_CONSTEXPR const_pointer data() const SPROUT_NOEXCEPT { \
+				return elems_.data(); \
+			} \
+			SPROUT_CXX14_CONSTEXPR pointer c_array() SPROUT_NOEXCEPT { \
+				return elems_.c_array(); \
+			} \
+			SPROUT_CONSTEXPR const_pointer c_array() const SPROUT_NOEXCEPT { \
+				return elems_.c_array(); \
+			}
+
+#define	SPROUT_QUATERNION_MEMBER_STATIC_SIZE_SPECIALIZATION_GENERATOR(type) \
+		SPROUT_CONSTEXPR_OR_CONST typename sprout::math::quaternion<type>::size_type sprout::math::quaternion<type>::static_size;
+
+		template<>
+		class quaternion<float> {
+		public:
+			SPROUT_QUATERNION_MEMBER_TYPE_DATA_GENERATOR(float)
+		public:
+			SPROUT_QUATERNION_CONSTRUCTOR_GENERATOR(float)
+			explicit SPROUT_CONSTEXPR quaternion(quaternion<double> const& a_recopier);
+			explicit SPROUT_CONSTEXPR quaternion(quaternion<long double> const& a_recopier);
+			SPROUT_QUATERNION_ACCESSOR_GENERATOR(float)
+			SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(float)
+			SPROUT_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(float)
+			SPROUT_QUATERNION_MEMBER_CONTAINER_GENERATOR(float)
+		};
+		SPROUT_QUATERNION_MEMBER_STATIC_SIZE_SPECIALIZATION_GENERATOR(float)
+
+		template<>
+		class quaternion<double> {
+		public:
+			SPROUT_QUATERNION_MEMBER_TYPE_DATA_GENERATOR(double)
+		public:
+			SPROUT_QUATERNION_CONSTRUCTOR_GENERATOR(double)
+			explicit SPROUT_CONSTEXPR quaternion(quaternion<float> const& a_recopier);
+			explicit SPROUT_CONSTEXPR quaternion(quaternion<long double> const& a_recopier);
+			SPROUT_QUATERNION_ACCESSOR_GENERATOR(double)
+			SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(double)
+			SPROUT_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(double)
+			SPROUT_QUATERNION_MEMBER_CONTAINER_GENERATOR(double)
+		};
+		SPROUT_QUATERNION_MEMBER_STATIC_SIZE_SPECIALIZATION_GENERATOR(double)
+
+		template<>
+		class quaternion<long double> {
+		public:
+			SPROUT_QUATERNION_MEMBER_TYPE_DATA_GENERATOR(long double)
+		public:
+			SPROUT_QUATERNION_CONSTRUCTOR_GENERATOR(long double)
+			explicit SPROUT_CONSTEXPR quaternion(quaternion<float> const& a_recopier);
+			explicit SPROUT_CONSTEXPR quaternion(quaternion<double> const& a_recopier);
+			SPROUT_QUATERNION_ACCESSOR_GENERATOR(long double)
+			SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(long double)
+			SPROUT_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(long double)
+			SPROUT_QUATERNION_MEMBER_CONTAINER_GENERATOR(long double)
+		};
+		SPROUT_QUATERNION_MEMBER_STATIC_SIZE_SPECIALIZATION_GENERATOR(long double)
+
+		SPROUT_CONSTEXPR sprout::math::quaternion<float>::quaternion(sprout::math::quaternion<double> const& a_recopier)
+			: elems_{{
+				static_cast<float>(a_recopier.R_component_1()),
+				static_cast<float>(a_recopier.R_component_2()),
+				static_cast<float>(a_recopier.R_component_3()),
+				static_cast<float>(a_recopier.R_component_4())
+				}}
+		{}
+		SPROUT_CONSTEXPR sprout::math::quaternion<float>::quaternion(sprout::math::quaternion<long double> const& a_recopier)
+			: elems_{{
+				static_cast<float>(a_recopier.R_component_1()),
+				static_cast<float>(a_recopier.R_component_2()),
+				static_cast<float>(a_recopier.R_component_3()),
+				static_cast<float>(a_recopier.R_component_4())
+				}}
+		{}
+
+		SPROUT_CONSTEXPR sprout::math::quaternion<double>::quaternion(sprout::math::quaternion<float> const& a_recopier)
+			: elems_{{
+				static_cast<double>(a_recopier.R_component_1()),
+				static_cast<double>(a_recopier.R_component_2()),
+				static_cast<double>(a_recopier.R_component_3()),
+				static_cast<double>(a_recopier.R_component_4())
+				}}
+		{}
+		SPROUT_CONSTEXPR sprout::math::quaternion<double>::quaternion(sprout::math::quaternion<long double> const& a_recopier)
+			: elems_{{
+				static_cast<double>(a_recopier.R_component_1()),
+				static_cast<double>(a_recopier.R_component_2()),
+				static_cast<double>(a_recopier.R_component_3()),
+				static_cast<double>(a_recopier.R_component_4())
+				}}
+		{}
+
+		SPROUT_CONSTEXPR sprout::math::quaternion<long double>::quaternion(sprout::math::quaternion<float> const& a_recopier)
+			: elems_{{
+				static_cast<long double>(a_recopier.R_component_1()),
+				static_cast<long double>(a_recopier.R_component_2()),
+				static_cast<long double>(a_recopier.R_component_3()),
+				static_cast<long double>(a_recopier.R_component_4())
+				}}
+		{}
+		SPROUT_CONSTEXPR sprout::math::quaternion<long double>::quaternion(sprout::math::quaternion<double> const& a_recopier)
+			: elems_{{
+				static_cast<long double>(a_recopier.R_component_1()),
+				static_cast<long double>(a_recopier.R_component_2()),
+				static_cast<long double>(a_recopier.R_component_3()),
+				static_cast<long double>(a_recopier.R_component_4())
+				}}
+		{}
+
+#undef	SPROUT_QUATERNION_MEMBER_CONTAINER_GENERATOR
+#undef	SPROUT_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR
+#undef	SPROUT_QUATERNION_MEMBER_ADD_GENERATOR
+#undef	SPROUT_QUATERNION_MEMBER_SUB_GENERATOR
+#undef	SPROUT_QUATERNION_MEMBER_MUL_GENERATOR
+#undef	SPROUT_QUATERNION_MEMBER_DIV_GENERATOR
+#undef	SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_1
+#undef	SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_2
+#undef	SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_3
+#undef	SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_1
+#undef	SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_2
+#undef	SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_3
+#undef	SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_1
+#undef	SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_2
+#undef	SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_3
+#undef	SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_1
+#undef	SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_2
+#undef	SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_3
+#undef	SPROUT_QUATERNION_CONSTRUCTOR_GENERATOR
+#undef	SPROUT_QUATERNION_MEMBER_TYPE_DATA_GENERATOR
+#undef	SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR
+#undef	SPROUT_QUATERNION_ACCESSOR_GENERATOR
+
+		//
+		// 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
+
+		//
+		// operator<<
+		// operator>>
+		//
+		template<typename T, typename Elem, typename Traits>
+		inline SPROUT_NON_CONSTEXPR std::basic_ostream<Elem, Traits>&
+		operator<<(	std::basic_ostream<Elem, Traits>& lhs, sprout::math::quaternion<T> const& rhs) {
+			std::basic_ostringstream<Elem, Traits> s;
+			s.flags(lhs.flags());
+			s.imbue(lhs.getloc());
+			s.precision(lhs.precision());
+			s
+				<< '('
+				<< rhs.R_component_1() << ','
+				<< rhs.R_component_2() << ','
+				<< rhs.R_component_3() << ','
+				<< rhs.R_component_4()
+				<< ')'
+				;
+			return lhs << s.str();
+		}
+		template<typename T, typename Elem, typename Traits>
+		inline SPROUT_NON_CONSTEXPR std::basic_istream<Elem, Traits>&
+		operator>>(std::basic_istream<Elem, Traits>& lhs, sprout::math::quaternion<T>& rhs) {
+			std::ctype<Elem> const& ct = std::use_facet<std::ctype<Elem> >(lhs.getloc());
+			T a = T();
+			T b = T();
+			T c = T();
+			T d = T();
+			sprout::complex<T> u = sprout::complex<T>();
+			sprout::complex<T> v = sprout::complex<T>();
+			Elem ch = Elem();
+			char cc;
+			lhs >> ch;
+			if (!lhs.good()) {
+				goto finish;
+			}
+			cc = ct.narrow(ch, char());
+			if (cc == '(') {
+				lhs >> ch;
+				if (!lhs.good()) {
+					goto finish;
+				}
+				cc = ct.narrow(ch, char());
+				if (cc == '(') {
+					lhs.putback(ch);
+					lhs >> u;
+					a = u.real();
+					b = u.imag();
+					if (!lhs.good()) {
+						goto finish;
+					}
+					lhs >> ch;
+					if (!lhs.good()) {
+						goto finish;
+					}
+					cc = ct.narrow(ch, char());
+					if (cc == ')') {
+						rhs = sprout::math::quaternion<T>(a, b);
+					} else if (cc == ',') {
+						lhs >> v;
+						c = v.real();
+						d = v.imag();
+						if (!lhs.good()) {
+							goto finish;
+						}
+						lhs >> ch;
+						if (!lhs.good()) {
+							goto finish;
+						}
+						cc = ct.narrow(ch, char());
+						if (cc == ')') {
+							rhs = sprout::math::quaternion<T>(a, b, c, d);
+						} else {
+							lhs.setstate(std::ios_base::failbit);
+						}
+					} else {
+						lhs.setstate(std::ios_base::failbit);
+					}
+				} else {
+					lhs.putback(ch);
+					lhs >> a;
+					if (!lhs.good()) {
+						goto finish;
+					}
+					lhs >> ch;
+					if (!lhs.good()) {
+						goto finish;
+					}
+					cc = ct.narrow(ch, char());
+					if (cc == ')') {
+						rhs = sprout::math::quaternion<T>(a);
+					} else if (cc == ',') {
+						lhs >> ch;
+						if (!lhs.good()) {
+							goto finish;
+						}
+						cc = ct.narrow(ch, char());
+						if (cc == '(') {
+							lhs.putback(ch);
+							lhs >> v;
+							c = v.real();
+							d = v.imag();
+							if (!lhs.good()) {
+								goto finish;
+							}
+							lhs >> ch;
+							if (!lhs.good()) {
+								goto finish;
+							}
+							cc = ct.narrow(ch, char());
+							if (cc == ')') {
+								rhs = sprout::math::quaternion<T>(a, b, c, d);
+							} else {
+								lhs.setstate(std::ios_base::failbit);
+							}
+						} else {
+							lhs.putback(ch);
+							lhs >> b;
+							if (!lhs.good()) {
+								goto finish;
+							}
+							lhs >> ch;
+							if (!lhs.good()) {
+								goto finish;
+							}
+							cc = ct.narrow(ch, char());
+							if (cc == ')') {
+								rhs = sprout::math::quaternion<T>(a, b);
+							} else if (cc == ',') {
+								lhs >> c;
+								if (!lhs.good()) {
+									goto finish;
+								}
+								lhs >> ch;
+								if (!lhs.good()) {
+									goto finish;
+								}
+								cc = ct.narrow(ch, char());
+								if (cc == ')') {
+									rhs = sprout::math::quaternion<T>(a, b, c);
+								} else if (cc == ',') {
+									lhs >> d;
+									if (!lhs.good()) {
+										goto finish;
+									}
+									lhs >> ch;
+									if (!lhs.good()) {
+										goto finish;
+									}
+									cc = ct.narrow(ch, char());
+									if (cc == ')') {
+										rhs = sprout::math::quaternion<T>(a, b, c, d);
+									} else {
+										lhs.setstate(std::ios_base::failbit);
+									}
+								} else {
+									lhs.setstate(std::ios_base::failbit);
+								}
+							} else {
+								lhs.setstate(std::ios_base::failbit);
+							}
+						}
+					} else {
+						lhs.setstate(std::ios_base::failbit);
+					}
+				}
+			} else {
+				lhs.putback(ch);
+				lhs >> a;
+				if (!lhs.good()) {
+					goto finish;
+				}
+				rhs = sprout::math::quaternion<T>(a);
+			}
+		finish:
+			return lhs;
+		}
+
+		//
+		// real
+		// unreal
+		//
+		template<typename T>
+		inline SPROUT_CONSTEXPR T
+		real(sprout::math::quaternion<T> const& q) {
+			return q.real();
+		}
+		template<typename T>
+		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+		unreal(sprout::math::quaternion<T> const& q) {
+			return q.unreal();
+		}
+
+		//
+		// sup
+		// l1
+		//
+		template<typename T>
+		inline SPROUT_CONSTEXPR T
+		sup(sprout::math::quaternion<T> const& q) {
+			return sprout::math::detail::abs_max(
+				sprout::array<T, 4>{{
+					q.R_component_1(),
+					q.R_component_2(),
+					q.R_component_3(),
+					q.R_component_4()
+					}}
+				);
+		}
+		template<typename T>
+		inline SPROUT_CONSTEXPR T
+		l1(sprout::math::quaternion<T> const& q) {
+			return sprout::math::detail::abs_sum(
+				sprout::array<T, 4>{{
+					q.R_component_1(),
+					q.R_component_2(),
+					q.R_component_3(),
+					q.R_component_4()
+					}}
+				);
+		}
+
+		//
+		// abs
+		//
+		namespace detail {
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			abs_q_impl_3(sprout::array<T, 4> const& temp, T const& maxim) {
+				return maxim * sprout::math::sqrt(sprout::math::detail::sum(sprout::math::detail::mul(temp, temp)));
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			abs_q_impl_2(sprout::array<T, 4> const& temp, T const& maxim) {
+				return sprout::math::detail::abs_q_impl_3(
+					sprout::math::detail::mul(temp, maxim), maxim
+					);
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			abs_q_impl_1(sprout::array<T, 4> const& temp, T const& maxim) {
+				return maxim == static_cast<T>(0) ? sprout::math::quaternion<T>(maxim)
+					: sprout::math::detail::abs_q_impl_2(
+						temp, static_cast<T>(1) / maxim
+						)
+					;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			abs_q_impl(sprout::array<T, 4> const& temp) {
+				return sprout::math::detail::abs_q_impl_1(
+					temp, sprout::math::detail::abs_max(temp)
+					);
+			}
+		}	// namespace detail
+		template<typename T>
+		inline SPROUT_CONSTEXPR T
+		abs(sprout::math::quaternion<T> const& q) {
+			return sprout::math::detail::abs_q_impl(
+				sprout::array<T, 4>{{
+					q.R_component_1(),
+					q.R_component_2(),
+					q.R_component_3(),
+					q.R_component_4()
+					}}
+				);
+		}
+
+#undef	SPROUT_QUATERNION_ARRAY_LOADER
+
+		//
+		// conj
+		// norm
+		//
+		template<typename T>
+		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+		conj(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()
+				);
+		}
+		template<typename T>
+		inline SPROUT_CONSTEXPR T
+		norm(sprout::math::quaternion<T> const& q) {
+			return sprout::math::real(q * sprout::math::conj(q));
+		}
+
+		//
+		// spherical
+		// semipolar
+		// multipolar
+		// cylindrospherical
+		// cylindrical
+		//
+		namespace detail {
+			template<typename T>
+			inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+			spherical_impl(T const& rho, T const& theta, T const& phi1, T const& phi2, T const& p1, T const& p2) {
+				return rho * sprout::math::quaternion<T>(
+					sprout::math::cos(theta) * (p2 * p1),
+					sprout::math::sin(theta) * (p2 * p1),
+					sprout::math::sin(phi1) * p2,
+					sprout::math::sin(phi2)
+					);
+			}
+		}	// namespace detail
+		template<typename T>
+		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+		spherical(T const& rho, T const& theta, T const& phi1, T const& phi2) {
+			return sprout::math::detail::spherical_impl(
+				rho, theta, phi1, phi2,
+				sprout::math::cos(phi1), sprout::math::cos(phi2)
+				);
+		}
+		template<typename T>
+		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+		semipolar(T const& rho, T const& alpha, T const& theta1, T const& theta2) {
+			return rho * sprout::math::quaternion<T>(
+				sprout::math::cos(alpha) * sprout::math::cos(theta1),
+				sprout::math::cos(alpha) * sprout::math::sin(theta1),
+				sprout::math::sin(alpha) * sprout::math::cos(theta2),
+				sprout::math::sin(alpha) * sprout::math::sin(theta2)
+				);
+		}
+		template<typename T>
+		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+		multipolar(T const& rho1, T const& theta1, T const& rho2, T const& theta2) {
+			return sprout::math::quaternion<T>(
+				rho1 * sprout::math::cos(theta1),
+				rho1 * sprout::math::sin(theta1),
+				rho2 * sprout::math::cos(theta2),
+				rho2 * sprout::math::sin(theta2)
+				);
+		}
+		template<typename T>
+		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+		cylindrospherical(T const& t, T const& radius, T const& longitude, T const& latitude) {
+			return sprout::math::quaternion<T>(
+				t,
+				radius * sprout::math::cos(longitude) * sprout::math::cos(latitude),
+				radius * sprout::math::sin(longitude) * sprout::math::cos(latitude),
+				radius * sprout::math::sin(latitude)
+				);
+		}
+		template<typename T>
+		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+		cylindrical(T const& r, T const& angle, T const& h1, T const& h2) {
+			return sprout::math::quaternion<T>(
+				r * sprout::math::cos(angle),
+				r * sprout::math::sin(angle),
+				h1,
+				h2
+				);
+		}
+
+		//
+		// exp
+		//
+		// !!!
+//		namespace detail {
+//			template<typename T>
+//			inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+//			exp_impl_1(sprout::math::quaternion<T> const& q, T const& z, T const& w) {
+//				return sprout::math::exp(sprout::math::real(q)) * sprout::math::quaternion<T>(
+//					sprout::math::cos(z),
+//					w * q.R_component_2(),
+//					w * q.R_component_3(),
+//					w * q.R_component_4()
+//					);
+//			}
+//			template<typename T>
+//			inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+//			exp_impl(sprout::math::quaternion<T> const& q, T const& z) {
+//				return sprout::math::detail::exp_impl_1(
+//					q, z,
+//					sprout::math::sinc_pi(z)
+//					);
+//			}
+//		}	// namespace detail
+//		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+//		exp(sprout::math::quaternion<T> const& q) {
+//			return sprout::math::detail::exp_impl(
+//				q,
+//				sprout::math::abs(sprout::math::unreal(q))
+//				);
+//		}
+
+		//
+		// cos
+		// sin
+		// tan
+		//
+		// !!!
+//		namespace detail {
+//			template<typename T>
+//			inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+//			cos_impl_1(sprout::math::quaternion<T> const& q, T const& z, T const& w) {
+//				return sprout::math::quaternion<T>(
+//					sprout::math::cos(q.real()) * sprout::math::cosh(z),
+//					w * q.R_component_2(),
+//					w * q.R_component_3(),
+//					w * q.R_component_4()
+//					);
+//			}
+//			template<typename T>
+//			inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+//			cos_impl(sprout::math::quaternion<T> const& q, T const& z) {
+//				return sprout::math::detail::cos_impl_1(
+//					q, z,
+//					-sprout::math::sin(q.real()) * sprout::math::sinhc_pi(z)
+//					);
+//			}
+//		}	// namespace detail
+//		template<typename T>
+//		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+//		cos(sprout::math::quaternion<T> const& q) {
+//			return sprout::math::detail::cos_impl(
+//				q,
+//				sprout::math::abs(sprout::math::unreal(q))
+//				);
+//		}
+//		namespace detail {
+//			template<typename T>
+//			inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+//			sin_impl_1(sprout::math::quaternion<T> const& q, T const& z, T const& w) {
+//				return sprout::math::quaternion<T>(
+//					sprout::math::sin(q.real()) * sprout::math::cosh(z),
+//					w * q.R_component_2(),
+//					w * q.R_component_3(),
+//					w * q.R_component_4()
+//					);
+//			}
+//			template<typename T>
+//			inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+//			sin_impl(sprout::math::quaternion<T> const& q, T const& z) {
+//				return sprout::math::detail::sin_impl_1(
+//					q, z,
+//					+sprout::math::cos(q.real()) * sprout::math::sinhc_pi(z)
+//					);
+//			}
+//		}	// namespace detail
+//		template<typename T>
+//		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+//		sin(sprout::math::quaternion<T> const& q) {
+//			return sprout::math::detail::sin_impl(
+//				q,
+//				sprout::math::abs(sprout::math::unreal(q))
+//				);
+//		}
+//		template<typename T>
+//		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+//		tan(sprout::math::quaternion<T> const& q) {
+//			return sprout::math::sin(q) / sprout::math::cos(q);
+//		}
+
+		//
+		// cosh
+		// sinh
+		// tanh
+		//
+		// !!!
+//		template<typename T>
+//		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+//		cosh(sprout::math::quaternion<T> const& q) {
+//			return (sprout::math::exp(+q) + sprout::math::exp(-q)) / static_cast<T>(2);
+//		}
+//		template<typename T>
+//		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+//		sinh(sprout::math::quaternion<T> const& q) {
+//			return (sprout::math::exp(+q) - sprout::math::exp(-q)) / static_cast<T>(2);
+//		}
+//		template<typename T>
+//		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+//		tanh(sprout::math::quaternion<T> const& q) {
+//			return sprout::math::sinh(q) / sprout::math::cosh(q);
+//		}
+
+		//
+		// pow
+		//
+		namespace detail {
+			template<typename T>
+			inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+			pow_q_impl(sprout::math::quaternion<T> const& q, int n, int	m, sprout::math::quaternion<T> const& result) {
+				return n != m << 1 ? result * result * q
+					: result * result
+					;
+			}
+		}	// namespace detail
+		template<typename T>
+		inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
+		pow(sprout::math::quaternion<T> const& q, int n) {
+			return n > 1 ? sprout::math::detail::pow_q_impl(
+					q, n, n >> 1, sprout::math::pow(q, n >> 1)
+					)
+				: n == 1 ? q
+				: n == 0 ? sprout::math::quaternion<T>(static_cast<T>(1))
+				: sprout::math::pow(sprout::math::quaternion<T>(static_cast<T>(1)) / q, -n)
+				;
+		}
+	}	// namespace math
+
+	using sprout::math::quaternion;
+	using sprout::math::real;
+	using sprout::math::unreal;
+	using sprout::math::sup;
+	using sprout::math::l1;
+	using sprout::math::abs;
+	using sprout::math::conj;
+	using sprout::math::norm;
+	using sprout::math::spherical;
+	using sprout::math::semipolar;
+	using sprout::math::multipolar;
+	using sprout::math::cylindrospherical;
+	using sprout::math::cylindrical;
+//	using sprout::math::exp;
+//	using sprout::math::cos;
+//	using sprout::math::sin;
+//	using sprout::math::tan;
+//	using sprout::math::cosh;
+//	using sprout::math::sinh;
+//	using sprout::math::tanh;
+	using sprout::math::pow;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_QUATERNION_QUATERNION_HPP