williamr@2: // boost quaternion.hpp header file williamr@2: williamr@2: // (C) Copyright Hubert Holin 2001. williamr@2: // Distributed under the Boost Software License, Version 1.0. (See williamr@2: // accompanying file LICENSE_1_0.txt or copy at williamr@2: // http://www.boost.org/LICENSE_1_0.txt) williamr@2: williamr@2: // See http://www.boost.org for updates, documentation, and revision history. williamr@2: williamr@2: #ifndef BOOST_QUATERNION_HPP williamr@2: #define BOOST_QUATERNION_HPP williamr@2: williamr@2: williamr@2: #include williamr@2: #include // for the "<<" and ">>" operators williamr@2: #include // for the "<<" operator williamr@2: williamr@2: #include // for BOOST_NO_STD_LOCALE williamr@2: #include williamr@2: #ifndef BOOST_NO_STD_LOCALE williamr@2: #include // for the "<<" operator williamr@2: #endif /* BOOST_NO_STD_LOCALE */ williamr@2: williamr@2: #include williamr@2: williamr@2: williamr@2: williamr@2: #include // for the Sinus cardinal williamr@2: #include // for the Hyperbolic Sinus cardinal williamr@2: williamr@2: williamr@2: namespace boost williamr@2: { williamr@2: namespace math williamr@2: { williamr@2: #if BOOST_WORKAROUND(__GNUC__, < 3) williamr@2: // gcc 2.95.x uses expression templates for valarray calculations, but williamr@2: // the result is not conforming. We need BOOST_GET_VALARRAY to get an williamr@2: // actual valarray result when we need to call a member function williamr@2: #define BOOST_GET_VALARRAY(T,x) ::std::valarray(x) williamr@2: // gcc 2.95.x has an "std::ios" class that is similar to williamr@2: // "std::ios_base", so we just use a #define williamr@2: #define BOOST_IOS_BASE ::std::ios williamr@2: // gcc 2.x ignores function scope using declarations, williamr@2: // put them in the scope of the enclosing namespace instead: williamr@2: using ::std::valarray; williamr@2: using ::std::sqrt; williamr@2: using ::std::cos; williamr@2: using ::std::sin; williamr@2: using ::std::exp; williamr@2: using ::std::cosh; williamr@2: #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ williamr@2: williamr@2: #define BOOST_QUATERNION_ACCESSOR_GENERATOR(type) \ williamr@2: type real() const \ williamr@2: { \ williamr@2: return(a); \ williamr@2: } \ williamr@2: \ williamr@2: quaternion unreal() const \ williamr@2: { \ williamr@2: return(quaternion(static_cast(0),b,c,d)); \ williamr@2: } \ williamr@2: \ williamr@2: type R_component_1() const \ williamr@2: { \ williamr@2: return(a); \ williamr@2: } \ williamr@2: \ williamr@2: type R_component_2() const \ williamr@2: { \ williamr@2: return(b); \ williamr@2: } \ williamr@2: \ williamr@2: type R_component_3() const \ williamr@2: { \ williamr@2: return(c); \ williamr@2: } \ williamr@2: \ williamr@2: type R_component_4() const \ williamr@2: { \ williamr@2: return(d); \ williamr@2: } \ williamr@2: \ williamr@2: ::std::complex C_component_1() const \ williamr@2: { \ williamr@2: return(::std::complex(a,b)); \ williamr@2: } \ williamr@2: \ williamr@2: ::std::complex C_component_2() const \ williamr@2: { \ williamr@2: return(::std::complex(c,d)); \ williamr@2: } williamr@2: williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(type) \ williamr@2: template \ williamr@2: quaternion & operator = (quaternion const & a_affecter) \ williamr@2: { \ williamr@2: a = static_cast(a_affecter.R_component_1()); \ williamr@2: b = static_cast(a_affecter.R_component_2()); \ williamr@2: c = static_cast(a_affecter.R_component_3()); \ williamr@2: d = static_cast(a_affecter.R_component_4()); \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } \ williamr@2: \ williamr@2: quaternion & operator = (quaternion const & a_affecter) \ williamr@2: { \ williamr@2: a = a_affecter.a; \ williamr@2: b = a_affecter.b; \ williamr@2: c = a_affecter.c; \ williamr@2: d = a_affecter.d; \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } \ williamr@2: \ williamr@2: quaternion & operator = (type const & a_affecter) \ williamr@2: { \ williamr@2: a = a_affecter; \ williamr@2: \ williamr@2: b = c = d = static_cast(0); \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } \ williamr@2: \ williamr@2: quaternion & operator = (::std::complex const & a_affecter) \ williamr@2: { \ williamr@2: a = a_affecter.real(); \ williamr@2: b = a_affecter.imag(); \ williamr@2: \ williamr@2: c = d = static_cast(0); \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_DATA_GENERATOR(type) \ williamr@2: type a; \ williamr@2: type b; \ williamr@2: type c; \ williamr@2: type d; williamr@2: williamr@2: williamr@2: template williamr@2: class quaternion williamr@2: { williamr@2: public: williamr@2: williamr@2: typedef T value_type; williamr@2: williamr@2: williamr@2: // constructor for H seen as R^4 williamr@2: // (also default constructor) williamr@2: williamr@2: explicit quaternion( T const & requested_a = T(), williamr@2: T const & requested_b = T(), williamr@2: T const & requested_c = T(), williamr@2: T const & requested_d = T()) williamr@2: : a(requested_a), williamr@2: b(requested_b), williamr@2: c(requested_c), williamr@2: d(requested_d) williamr@2: { williamr@2: // nothing to do! williamr@2: } williamr@2: williamr@2: williamr@2: // constructor for H seen as C^2 williamr@2: williamr@2: explicit quaternion( ::std::complex const & z0, williamr@2: ::std::complex const & z1 = ::std::complex()) williamr@2: : a(z0.real()), williamr@2: b(z0.imag()), williamr@2: c(z1.real()), williamr@2: d(z1.imag()) williamr@2: { williamr@2: // nothing to do! williamr@2: } williamr@2: williamr@2: williamr@2: // UNtemplated copy constructor williamr@2: // (this is taken care of by the compiler itself) williamr@2: williamr@2: williamr@2: // templated copy constructor williamr@2: williamr@2: template williamr@2: explicit quaternion(quaternion const & a_recopier) williamr@2: : a(static_cast(a_recopier.R_component_1())), williamr@2: b(static_cast(a_recopier.R_component_2())), williamr@2: c(static_cast(a_recopier.R_component_3())), williamr@2: d(static_cast(a_recopier.R_component_4())) williamr@2: { williamr@2: // nothing to do! williamr@2: } williamr@2: williamr@2: williamr@2: // destructor williamr@2: // (this is taken care of by the compiler itself) williamr@2: williamr@2: williamr@2: // accessors williamr@2: // williamr@2: // Note: Like complex number, quaternions do have a meaningful notion of "real part", williamr@2: // but unlike them there is no meaningful notion of "imaginary part". williamr@2: // Instead there is an "unreal part" which itself is a quaternion, and usually williamr@2: // nothing simpler (as opposed to the complex number case). williamr@2: // However, for practicallity, there are accessors for the other components williamr@2: // (these are necessary for the templated copy constructor, for instance). williamr@2: williamr@2: BOOST_QUATERNION_ACCESSOR_GENERATOR(T) williamr@2: williamr@2: // assignment operators williamr@2: williamr@2: BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(T) williamr@2: williamr@2: // other assignment-related operators williamr@2: // williamr@2: // NOTE: Quaternion multiplication is *NOT* commutative; williamr@2: // symbolically, "q *= rhs;" means "q = q * rhs;" williamr@2: // and "q /= rhs;" means "q = q * inverse_of(rhs);" williamr@2: williamr@2: quaternion & operator += (T const & rhs) williamr@2: { williamr@2: T at = a + rhs; // exception guard williamr@2: williamr@2: a = at; williamr@2: williamr@2: return(*this); williamr@2: } williamr@2: williamr@2: williamr@2: quaternion & operator += (::std::complex const & rhs) williamr@2: { williamr@2: T at = a + rhs.real(); // exception guard williamr@2: T bt = b + rhs.imag(); // exception guard williamr@2: williamr@2: a = at; williamr@2: b = bt; williamr@2: williamr@2: return(*this); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: quaternion & operator += (quaternion const & rhs) williamr@2: { williamr@2: T at = a + static_cast(rhs.R_component_1()); // exception guard williamr@2: T bt = b + static_cast(rhs.R_component_2()); // exception guard williamr@2: T ct = c + static_cast(rhs.R_component_3()); // exception guard williamr@2: T dt = d + static_cast(rhs.R_component_4()); // exception guard williamr@2: williamr@2: a = at; williamr@2: b = bt; williamr@2: c = ct; williamr@2: d = dt; williamr@2: williamr@2: return(*this); williamr@2: } williamr@2: williamr@2: williamr@2: williamr@2: quaternion & operator -= (T const & rhs) williamr@2: { williamr@2: T at = a - rhs; // exception guard williamr@2: williamr@2: a = at; williamr@2: williamr@2: return(*this); williamr@2: } williamr@2: williamr@2: williamr@2: quaternion & operator -= (::std::complex const & rhs) williamr@2: { williamr@2: T at = a - rhs.real(); // exception guard williamr@2: T bt = b - rhs.imag(); // exception guard williamr@2: williamr@2: a = at; williamr@2: b = bt; williamr@2: williamr@2: return(*this); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: quaternion & operator -= (quaternion const & rhs) williamr@2: { williamr@2: T at = a - static_cast(rhs.R_component_1()); // exception guard williamr@2: T bt = b - static_cast(rhs.R_component_2()); // exception guard williamr@2: T ct = c - static_cast(rhs.R_component_3()); // exception guard williamr@2: T dt = d - static_cast(rhs.R_component_4()); // exception guard williamr@2: williamr@2: a = at; williamr@2: b = bt; williamr@2: c = ct; williamr@2: d = dt; williamr@2: williamr@2: return(*this); williamr@2: } williamr@2: williamr@2: williamr@2: quaternion & operator *= (T const & rhs) williamr@2: { williamr@2: T at = a * rhs; // exception guard williamr@2: T bt = b * rhs; // exception guard williamr@2: T ct = c * rhs; // exception guard williamr@2: T dt = d * rhs; // exception guard williamr@2: williamr@2: a = at; williamr@2: b = bt; williamr@2: c = ct; williamr@2: d = dt; williamr@2: williamr@2: return(*this); williamr@2: } williamr@2: williamr@2: williamr@2: quaternion & operator *= (::std::complex const & rhs) williamr@2: { williamr@2: T ar = rhs.real(); williamr@2: T br = rhs.imag(); williamr@2: williamr@2: T at = +a*ar-b*br; williamr@2: T bt = +a*br+b*ar; williamr@2: T ct = +c*ar+d*br; williamr@2: T dt = -c*br+d*ar; williamr@2: williamr@2: a = at; williamr@2: b = bt; williamr@2: c = ct; williamr@2: d = dt; williamr@2: williamr@2: return(*this); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: quaternion & operator *= (quaternion const & rhs) williamr@2: { williamr@2: T ar = static_cast(rhs.R_component_1()); williamr@2: T br = static_cast(rhs.R_component_2()); williamr@2: T cr = static_cast(rhs.R_component_3()); williamr@2: T dr = static_cast(rhs.R_component_4()); williamr@2: williamr@2: T at = +a*ar-b*br-c*cr-d*dr; williamr@2: T bt = +a*br+b*ar+c*dr-d*cr; //(a*br+ar*b)+(c*dr-cr*d); williamr@2: T ct = +a*cr-b*dr+c*ar+d*br; //(a*cr+ar*c)+(d*br-dr*b); williamr@2: T dt = +a*dr+b*cr-c*br+d*ar; //(a*dr+ar*d)+(b*cr-br*c); williamr@2: williamr@2: a = at; williamr@2: b = bt; williamr@2: c = ct; williamr@2: d = dt; williamr@2: williamr@2: return(*this); williamr@2: } williamr@2: williamr@2: williamr@2: williamr@2: quaternion & operator /= (T const & rhs) williamr@2: { williamr@2: T at = a / rhs; // exception guard williamr@2: T bt = b / rhs; // exception guard williamr@2: T ct = c / rhs; // exception guard williamr@2: T dt = d / rhs; // exception guard williamr@2: williamr@2: a = at; williamr@2: b = bt; williamr@2: c = ct; williamr@2: d = dt; williamr@2: williamr@2: return(*this); williamr@2: } williamr@2: williamr@2: williamr@2: quaternion & operator /= (::std::complex const & rhs) williamr@2: { williamr@2: T ar = rhs.real(); williamr@2: T br = rhs.imag(); williamr@2: williamr@2: T denominator = ar*ar+br*br; williamr@2: williamr@2: T at = (+a*ar+b*br)/denominator; //(a*ar+b*br)/denominator; williamr@2: T bt = (-a*br+b*ar)/denominator; //(ar*b-a*br)/denominator; williamr@2: T ct = (+c*ar-d*br)/denominator; //(ar*c-d*br)/denominator; williamr@2: T dt = (+c*br+d*ar)/denominator; //(ar*d+br*c)/denominator; williamr@2: williamr@2: a = at; williamr@2: b = bt; williamr@2: c = ct; williamr@2: d = dt; williamr@2: williamr@2: return(*this); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: quaternion & operator /= (quaternion const & rhs) williamr@2: { williamr@2: T ar = static_cast(rhs.R_component_1()); williamr@2: T br = static_cast(rhs.R_component_2()); williamr@2: T cr = static_cast(rhs.R_component_3()); williamr@2: T dr = static_cast(rhs.R_component_4()); williamr@2: williamr@2: T denominator = ar*ar+br*br+cr*cr+dr*dr; williamr@2: williamr@2: T at = (+a*ar+b*br+c*cr+d*dr)/denominator; //(a*ar+b*br+c*cr+d*dr)/denominator; williamr@2: T bt = (-a*br+b*ar-c*dr+d*cr)/denominator; //((ar*b-a*br)+(cr*d-c*dr))/denominator; williamr@2: T ct = (-a*cr+b*dr+c*ar-d*br)/denominator; //((ar*c-a*cr)+(dr*b-d*br))/denominator; williamr@2: T dt = (-a*dr-b*cr+c*br+d*ar)/denominator; //((ar*d-a*dr)+(br*c-b*cr))/denominator; williamr@2: williamr@2: a = at; williamr@2: b = bt; williamr@2: c = ct; williamr@2: d = dt; williamr@2: williamr@2: return(*this); williamr@2: } williamr@2: williamr@2: williamr@2: protected: williamr@2: williamr@2: BOOST_QUATERNION_MEMBER_DATA_GENERATOR(T) williamr@2: williamr@2: williamr@2: private: williamr@2: williamr@2: }; williamr@2: williamr@2: williamr@2: // declaration of quaternion specialization williamr@2: williamr@2: template<> class quaternion; williamr@2: template<> class quaternion; williamr@2: template<> class quaternion; williamr@2: williamr@2: williamr@2: // helper templates for converting copy constructors (declaration) williamr@2: williamr@2: namespace detail williamr@2: { williamr@2: williamr@2: template< typename T, williamr@2: typename U williamr@2: > williamr@2: quaternion quaternion_type_converter(quaternion const & rhs); williamr@2: } williamr@2: williamr@2: williamr@2: // implementation of quaternion specialization williamr@2: williamr@2: williamr@2: #define BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(type) \ williamr@2: explicit quaternion( type const & requested_a = static_cast(0), \ williamr@2: type const & requested_b = static_cast(0), \ williamr@2: type const & requested_c = static_cast(0), \ williamr@2: type const & requested_d = static_cast(0)) \ williamr@2: : a(requested_a), \ williamr@2: b(requested_b), \ williamr@2: c(requested_c), \ williamr@2: d(requested_d) \ williamr@2: { \ williamr@2: } \ williamr@2: \ williamr@2: explicit quaternion( ::std::complex const & z0, \ williamr@2: ::std::complex const & z1 = ::std::complex()) \ williamr@2: : a(z0.real()), \ williamr@2: b(z0.imag()), \ williamr@2: c(z1.real()), \ williamr@2: d(z1.imag()) \ williamr@2: { \ williamr@2: } williamr@2: williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_ADD_GENERATOR_1(type) \ williamr@2: quaternion & operator += (type const & rhs) \ williamr@2: { \ williamr@2: a += rhs; \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_ADD_GENERATOR_2(type) \ williamr@2: quaternion & operator += (::std::complex const & rhs) \ williamr@2: { \ williamr@2: a += rhs.real(); \ williamr@2: b += rhs.imag(); \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_ADD_GENERATOR_3(type) \ williamr@2: template \ williamr@2: quaternion & operator += (quaternion const & rhs) \ williamr@2: { \ williamr@2: a += static_cast(rhs.R_component_1()); \ williamr@2: b += static_cast(rhs.R_component_2()); \ williamr@2: c += static_cast(rhs.R_component_3()); \ williamr@2: d += static_cast(rhs.R_component_4()); \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_SUB_GENERATOR_1(type) \ williamr@2: quaternion & operator -= (type const & rhs) \ williamr@2: { \ williamr@2: a -= rhs; \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_SUB_GENERATOR_2(type) \ williamr@2: quaternion & operator -= (::std::complex const & rhs) \ williamr@2: { \ williamr@2: a -= rhs.real(); \ williamr@2: b -= rhs.imag(); \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_SUB_GENERATOR_3(type) \ williamr@2: template \ williamr@2: quaternion & operator -= (quaternion const & rhs) \ williamr@2: { \ williamr@2: a -= static_cast(rhs.R_component_1()); \ williamr@2: b -= static_cast(rhs.R_component_2()); \ williamr@2: c -= static_cast(rhs.R_component_3()); \ williamr@2: d -= static_cast(rhs.R_component_4()); \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_MUL_GENERATOR_1(type) \ williamr@2: quaternion & operator *= (type const & rhs) \ williamr@2: { \ williamr@2: a *= rhs; \ williamr@2: b *= rhs; \ williamr@2: c *= rhs; \ williamr@2: d *= rhs; \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_MUL_GENERATOR_2(type) \ williamr@2: quaternion & operator *= (::std::complex const & rhs) \ williamr@2: { \ williamr@2: type ar = rhs.real(); \ williamr@2: type br = rhs.imag(); \ williamr@2: \ williamr@2: type at = +a*ar-b*br; \ williamr@2: type bt = +a*br+b*ar; \ williamr@2: type ct = +c*ar+d*br; \ williamr@2: type dt = -c*br+d*ar; \ williamr@2: \ williamr@2: a = at; \ williamr@2: b = bt; \ williamr@2: c = ct; \ williamr@2: d = dt; \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_MUL_GENERATOR_3(type) \ williamr@2: template \ williamr@2: quaternion & operator *= (quaternion const & rhs) \ williamr@2: { \ williamr@2: type ar = static_cast(rhs.R_component_1()); \ williamr@2: type br = static_cast(rhs.R_component_2()); \ williamr@2: type cr = static_cast(rhs.R_component_3()); \ williamr@2: type dr = static_cast(rhs.R_component_4()); \ williamr@2: \ williamr@2: type at = +a*ar-b*br-c*cr-d*dr; \ williamr@2: type bt = +a*br+b*ar+c*dr-d*cr; \ williamr@2: type ct = +a*cr-b*dr+c*ar+d*br; \ williamr@2: type dt = +a*dr+b*cr-c*br+d*ar; \ williamr@2: \ williamr@2: a = at; \ williamr@2: b = bt; \ williamr@2: c = ct; \ williamr@2: d = dt; \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: williamr@2: // There is quite a lot of repetition in the code below. This is intentional. williamr@2: // The last conditional block is the normal form, and the others merely williamr@2: // consist of workarounds for various compiler deficiencies. Hopefuly, when williamr@2: // more compilers are conformant and we can retire support for those that are williamr@2: // not, we will be able to remove the clutter. This is makes the situation williamr@2: // (painfully) explicit. williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_1(type) \ williamr@2: quaternion & operator /= (type const & rhs) \ williamr@2: { \ williamr@2: a /= rhs; \ williamr@2: b /= rhs; \ williamr@2: c /= rhs; \ williamr@2: d /= rhs; \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: williamr@2: #if defined(__GNUC__) && (__GNUC__ < 3) williamr@2: #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \ williamr@2: quaternion & operator /= (::std::complex const & rhs) \ williamr@2: { \ williamr@2: using ::std::valarray; \ williamr@2: \ williamr@2: valarray tr(2); \ williamr@2: \ williamr@2: tr[0] = rhs.real(); \ williamr@2: tr[1] = rhs.imag(); \ williamr@2: \ williamr@2: type mixam = (BOOST_GET_VALARRAY(type,static_cast(1)/abs(tr)).max)(); \ williamr@2: \ williamr@2: tr *= mixam; \ williamr@2: \ williamr@2: valarray tt(4); \ williamr@2: \ williamr@2: tt[0] = +a*tr[0]+b*tr[1]; \ williamr@2: tt[1] = -a*tr[1]+b*tr[0]; \ williamr@2: tt[2] = +c*tr[0]-d*tr[1]; \ williamr@2: tt[3] = +c*tr[1]+d*tr[0]; \ williamr@2: \ williamr@2: tr *= tr; \ williamr@2: \ williamr@2: tt *= (mixam/tr.sum()); \ williamr@2: \ williamr@2: a = tt[0]; \ williamr@2: b = tt[1]; \ williamr@2: c = tt[2]; \ williamr@2: d = tt[3]; \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: #elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) williamr@2: #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \ williamr@2: quaternion & operator /= (::std::complex const & rhs) \ williamr@2: { \ williamr@2: using ::std::valarray; \ williamr@2: using ::std::abs; \ williamr@2: \ williamr@2: valarray tr(2); \ williamr@2: \ williamr@2: tr[0] = rhs.real(); \ williamr@2: tr[1] = rhs.imag(); \ williamr@2: \ williamr@2: type mixam = static_cast(1)/(abs(tr).max)(); \ williamr@2: \ williamr@2: tr *= mixam; \ williamr@2: \ williamr@2: valarray tt(4); \ williamr@2: \ williamr@2: tt[0] = +a*tr[0]+b*tr[1]; \ williamr@2: tt[1] = -a*tr[1]+b*tr[0]; \ williamr@2: tt[2] = +c*tr[0]-d*tr[1]; \ williamr@2: tt[3] = +c*tr[1]+d*tr[0]; \ williamr@2: \ williamr@2: tr *= tr; \ williamr@2: \ williamr@2: tt *= (mixam/tr.sum()); \ williamr@2: \ williamr@2: a = tt[0]; \ williamr@2: b = tt[1]; \ williamr@2: c = tt[2]; \ williamr@2: d = tt[3]; \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: #else williamr@2: #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \ williamr@2: quaternion & operator /= (::std::complex const & rhs) \ williamr@2: { \ williamr@2: using ::std::valarray; \ williamr@2: \ williamr@2: valarray tr(2); \ williamr@2: \ williamr@2: tr[0] = rhs.real(); \ williamr@2: tr[1] = rhs.imag(); \ williamr@2: \ williamr@2: type mixam = static_cast(1)/(abs(tr).max)(); \ williamr@2: \ williamr@2: tr *= mixam; \ williamr@2: \ williamr@2: valarray tt(4); \ williamr@2: \ williamr@2: tt[0] = +a*tr[0]+b*tr[1]; \ williamr@2: tt[1] = -a*tr[1]+b*tr[0]; \ williamr@2: tt[2] = +c*tr[0]-d*tr[1]; \ williamr@2: tt[3] = +c*tr[1]+d*tr[0]; \ williamr@2: \ williamr@2: tr *= tr; \ williamr@2: \ williamr@2: tt *= (mixam/tr.sum()); \ williamr@2: \ williamr@2: a = tt[0]; \ williamr@2: b = tt[1]; \ williamr@2: c = tt[2]; \ williamr@2: d = tt[3]; \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: #endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ williamr@2: williamr@2: #if defined(__GNUC__) && (__GNUC__ < 3) williamr@2: #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type) \ williamr@2: template \ williamr@2: quaternion & operator /= (quaternion const & rhs) \ williamr@2: { \ williamr@2: using ::std::valarray; \ williamr@2: \ williamr@2: valarray tr(4); \ williamr@2: \ williamr@2: tr[0] = static_cast(rhs.R_component_1()); \ williamr@2: tr[1] = static_cast(rhs.R_component_2()); \ williamr@2: tr[2] = static_cast(rhs.R_component_3()); \ williamr@2: tr[3] = static_cast(rhs.R_component_4()); \ williamr@2: \ williamr@2: type mixam = (BOOST_GET_VALARRAY(type,static_cast(1)/abs(tr)).max)(); \ williamr@2: \ williamr@2: tr *= mixam; \ williamr@2: \ williamr@2: valarray tt(4); \ williamr@2: \ williamr@2: tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \ williamr@2: tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \ williamr@2: tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \ williamr@2: tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \ williamr@2: \ williamr@2: tr *= tr; \ williamr@2: \ williamr@2: tt *= (mixam/tr.sum()); \ williamr@2: \ williamr@2: a = tt[0]; \ williamr@2: b = tt[1]; \ williamr@2: c = tt[2]; \ williamr@2: d = tt[3]; \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: #elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) williamr@2: #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type) \ williamr@2: template \ williamr@2: quaternion & operator /= (quaternion const & rhs) \ williamr@2: { \ williamr@2: using ::std::valarray; \ williamr@2: using ::std::abs; \ williamr@2: \ williamr@2: valarray tr(4); \ williamr@2: \ williamr@2: tr[0] = static_cast(rhs.R_component_1()); \ williamr@2: tr[1] = static_cast(rhs.R_component_2()); \ williamr@2: tr[2] = static_cast(rhs.R_component_3()); \ williamr@2: tr[3] = static_cast(rhs.R_component_4()); \ williamr@2: \ williamr@2: type mixam = static_cast(1)/(abs(tr).max)(); \ williamr@2: \ williamr@2: tr *= mixam; \ williamr@2: \ williamr@2: valarray tt(4); \ williamr@2: \ williamr@2: tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \ williamr@2: tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \ williamr@2: tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \ williamr@2: tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \ williamr@2: \ williamr@2: tr *= tr; \ williamr@2: \ williamr@2: tt *= (mixam/tr.sum()); \ williamr@2: \ williamr@2: a = tt[0]; \ williamr@2: b = tt[1]; \ williamr@2: c = tt[2]; \ williamr@2: d = tt[3]; \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: #else williamr@2: #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type) \ williamr@2: template \ williamr@2: quaternion & operator /= (quaternion const & rhs) \ williamr@2: { \ williamr@2: using ::std::valarray; \ williamr@2: \ williamr@2: valarray tr(4); \ williamr@2: \ williamr@2: tr[0] = static_cast(rhs.R_component_1()); \ williamr@2: tr[1] = static_cast(rhs.R_component_2()); \ williamr@2: tr[2] = static_cast(rhs.R_component_3()); \ williamr@2: tr[3] = static_cast(rhs.R_component_4()); \ williamr@2: \ williamr@2: type mixam = static_cast(1)/(abs(tr).max)(); \ williamr@2: \ williamr@2: tr *= mixam; \ williamr@2: \ williamr@2: valarray tt(4); \ williamr@2: \ williamr@2: tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \ williamr@2: tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \ williamr@2: tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \ williamr@2: tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \ williamr@2: \ williamr@2: tr *= tr; \ williamr@2: \ williamr@2: tt *= (mixam/tr.sum()); \ williamr@2: \ williamr@2: a = tt[0]; \ williamr@2: b = tt[1]; \ williamr@2: c = tt[2]; \ williamr@2: d = tt[3]; \ williamr@2: \ williamr@2: return(*this); \ williamr@2: } williamr@2: #endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_ADD_GENERATOR(type) \ williamr@2: BOOST_QUATERNION_MEMBER_ADD_GENERATOR_1(type) \ williamr@2: BOOST_QUATERNION_MEMBER_ADD_GENERATOR_2(type) \ williamr@2: BOOST_QUATERNION_MEMBER_ADD_GENERATOR_3(type) williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_SUB_GENERATOR(type) \ williamr@2: BOOST_QUATERNION_MEMBER_SUB_GENERATOR_1(type) \ williamr@2: BOOST_QUATERNION_MEMBER_SUB_GENERATOR_2(type) \ williamr@2: BOOST_QUATERNION_MEMBER_SUB_GENERATOR_3(type) williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_MUL_GENERATOR(type) \ williamr@2: BOOST_QUATERNION_MEMBER_MUL_GENERATOR_1(type) \ williamr@2: BOOST_QUATERNION_MEMBER_MUL_GENERATOR_2(type) \ williamr@2: BOOST_QUATERNION_MEMBER_MUL_GENERATOR_3(type) williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR(type) \ williamr@2: BOOST_QUATERNION_MEMBER_DIV_GENERATOR_1(type) \ williamr@2: BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \ williamr@2: BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type) williamr@2: williamr@2: #define BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(type) \ williamr@2: BOOST_QUATERNION_MEMBER_ADD_GENERATOR(type) \ williamr@2: BOOST_QUATERNION_MEMBER_SUB_GENERATOR(type) \ williamr@2: BOOST_QUATERNION_MEMBER_MUL_GENERATOR(type) \ williamr@2: BOOST_QUATERNION_MEMBER_DIV_GENERATOR(type) williamr@2: williamr@2: williamr@2: template<> williamr@2: class quaternion williamr@2: { williamr@2: public: williamr@2: williamr@2: typedef float value_type; williamr@2: williamr@2: BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(float) williamr@2: williamr@2: // UNtemplated copy constructor williamr@2: // (this is taken care of by the compiler itself) williamr@2: williamr@2: // explicit copy constructors (precision-loosing converters) williamr@2: williamr@2: explicit quaternion(quaternion const & a_recopier) williamr@2: { williamr@2: *this = detail::quaternion_type_converter(a_recopier); williamr@2: } williamr@2: williamr@2: explicit quaternion(quaternion const & a_recopier) williamr@2: { williamr@2: *this = detail::quaternion_type_converter(a_recopier); williamr@2: } williamr@2: williamr@2: // destructor williamr@2: // (this is taken care of by the compiler itself) williamr@2: williamr@2: // accessors williamr@2: // williamr@2: // Note: Like complex number, quaternions do have a meaningful notion of "real part", williamr@2: // but unlike them there is no meaningful notion of "imaginary part". williamr@2: // Instead there is an "unreal part" which itself is a quaternion, and usually williamr@2: // nothing simpler (as opposed to the complex number case). williamr@2: // However, for practicallity, there are accessors for the other components williamr@2: // (these are necessary for the templated copy constructor, for instance). williamr@2: williamr@2: BOOST_QUATERNION_ACCESSOR_GENERATOR(float) williamr@2: williamr@2: // assignment operators williamr@2: williamr@2: BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(float) williamr@2: williamr@2: // other assignment-related operators williamr@2: // williamr@2: // NOTE: Quaternion multiplication is *NOT* commutative; williamr@2: // symbolically, "q *= rhs;" means "q = q * rhs;" williamr@2: // and "q /= rhs;" means "q = q * inverse_of(rhs);" williamr@2: williamr@2: BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(float) williamr@2: williamr@2: williamr@2: protected: williamr@2: williamr@2: BOOST_QUATERNION_MEMBER_DATA_GENERATOR(float) williamr@2: williamr@2: williamr@2: private: williamr@2: williamr@2: }; williamr@2: williamr@2: williamr@2: template<> williamr@2: class quaternion williamr@2: { williamr@2: public: williamr@2: williamr@2: typedef double value_type; williamr@2: williamr@2: BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(double) williamr@2: williamr@2: // UNtemplated copy constructor williamr@2: // (this is taken care of by the compiler itself) williamr@2: williamr@2: // converting copy constructor williamr@2: williamr@2: explicit quaternion(quaternion const & a_recopier) williamr@2: { williamr@2: *this = detail::quaternion_type_converter(a_recopier); williamr@2: } williamr@2: williamr@2: // explicit copy constructors (precision-loosing converters) williamr@2: williamr@2: explicit quaternion(quaternion const & a_recopier) williamr@2: { williamr@2: *this = detail::quaternion_type_converter(a_recopier); williamr@2: } williamr@2: williamr@2: // destructor williamr@2: // (this is taken care of by the compiler itself) williamr@2: williamr@2: // accessors williamr@2: // williamr@2: // Note: Like complex number, quaternions do have a meaningful notion of "real part", williamr@2: // but unlike them there is no meaningful notion of "imaginary part". williamr@2: // Instead there is an "unreal part" which itself is a quaternion, and usually williamr@2: // nothing simpler (as opposed to the complex number case). williamr@2: // However, for practicallity, there are accessors for the other components williamr@2: // (these are necessary for the templated copy constructor, for instance). williamr@2: williamr@2: BOOST_QUATERNION_ACCESSOR_GENERATOR(double) williamr@2: williamr@2: // assignment operators williamr@2: williamr@2: BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(double) williamr@2: williamr@2: // other assignment-related operators williamr@2: // williamr@2: // NOTE: Quaternion multiplication is *NOT* commutative; williamr@2: // symbolically, "q *= rhs;" means "q = q * rhs;" williamr@2: // and "q /= rhs;" means "q = q * inverse_of(rhs);" williamr@2: williamr@2: BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(double) williamr@2: williamr@2: williamr@2: protected: williamr@2: williamr@2: BOOST_QUATERNION_MEMBER_DATA_GENERATOR(double) williamr@2: williamr@2: williamr@2: private: williamr@2: williamr@2: }; williamr@2: williamr@2: williamr@2: template<> williamr@2: class quaternion williamr@2: { williamr@2: public: williamr@2: williamr@2: typedef long double value_type; williamr@2: williamr@2: BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(long double) williamr@2: williamr@2: // UNtemplated copy constructor williamr@2: // (this is taken care of by the compiler itself) williamr@2: williamr@2: // converting copy constructors williamr@2: williamr@2: explicit quaternion(quaternion const & a_recopier) williamr@2: { williamr@2: *this = detail::quaternion_type_converter(a_recopier); williamr@2: } williamr@2: williamr@2: explicit quaternion(quaternion const & a_recopier) williamr@2: { williamr@2: *this = detail::quaternion_type_converter(a_recopier); williamr@2: } williamr@2: williamr@2: // destructor williamr@2: // (this is taken care of by the compiler itself) williamr@2: williamr@2: // accessors williamr@2: // williamr@2: // Note: Like complex number, quaternions do have a meaningful notion of "real part", williamr@2: // but unlike them there is no meaningful notion of "imaginary part". williamr@2: // Instead there is an "unreal part" which itself is a quaternion, and usually williamr@2: // nothing simpler (as opposed to the complex number case). williamr@2: // However, for practicallity, there are accessors for the other components williamr@2: // (these are necessary for the templated copy constructor, for instance). williamr@2: williamr@2: BOOST_QUATERNION_ACCESSOR_GENERATOR(long double) williamr@2: williamr@2: // assignment operators williamr@2: williamr@2: BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(long double) williamr@2: williamr@2: // other assignment-related operators williamr@2: // williamr@2: // NOTE: Quaternion multiplication is *NOT* commutative; williamr@2: // symbolically, "q *= rhs;" means "q = q * rhs;" williamr@2: // and "q /= rhs;" means "q = q * inverse_of(rhs);" williamr@2: williamr@2: BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(long double) williamr@2: williamr@2: williamr@2: protected: williamr@2: williamr@2: BOOST_QUATERNION_MEMBER_DATA_GENERATOR(long double) williamr@2: williamr@2: williamr@2: private: williamr@2: williamr@2: }; williamr@2: williamr@2: williamr@2: #undef BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR williamr@2: #undef BOOST_QUATERNION_MEMBER_ADD_GENERATOR williamr@2: #undef BOOST_QUATERNION_MEMBER_SUB_GENERATOR williamr@2: #undef BOOST_QUATERNION_MEMBER_MUL_GENERATOR williamr@2: #undef BOOST_QUATERNION_MEMBER_DIV_GENERATOR williamr@2: #undef BOOST_QUATERNION_MEMBER_ADD_GENERATOR_1 williamr@2: #undef BOOST_QUATERNION_MEMBER_ADD_GENERATOR_2 williamr@2: #undef BOOST_QUATERNION_MEMBER_ADD_GENERATOR_3 williamr@2: #undef BOOST_QUATERNION_MEMBER_SUB_GENERATOR_1 williamr@2: #undef BOOST_QUATERNION_MEMBER_SUB_GENERATOR_2 williamr@2: #undef BOOST_QUATERNION_MEMBER_SUB_GENERATOR_3 williamr@2: #undef BOOST_QUATERNION_MEMBER_MUL_GENERATOR_1 williamr@2: #undef BOOST_QUATERNION_MEMBER_MUL_GENERATOR_2 williamr@2: #undef BOOST_QUATERNION_MEMBER_MUL_GENERATOR_3 williamr@2: #undef BOOST_QUATERNION_MEMBER_DIV_GENERATOR_1 williamr@2: #undef BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2 williamr@2: #undef BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3 williamr@2: williamr@2: #undef BOOST_QUATERNION_CONSTRUCTOR_GENERATOR williamr@2: williamr@2: williamr@2: #undef BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR williamr@2: williamr@2: #undef BOOST_QUATERNION_MEMBER_DATA_GENERATOR williamr@2: williamr@2: #undef BOOST_QUATERNION_ACCESSOR_GENERATOR williamr@2: williamr@2: williamr@2: // operators williamr@2: williamr@2: #define BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) \ williamr@2: { \ williamr@2: quaternion res(lhs); \ williamr@2: res op##= rhs; \ williamr@2: return(res); \ williamr@2: } williamr@2: williamr@2: #define BOOST_QUATERNION_OPERATOR_GENERATOR_1_L(op) \ williamr@2: template \ williamr@2: inline quaternion operator op (T const & lhs, quaternion const & rhs) \ williamr@2: BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) williamr@2: williamr@2: #define BOOST_QUATERNION_OPERATOR_GENERATOR_1_R(op) \ williamr@2: template \ williamr@2: inline quaternion operator op (quaternion const & lhs, T const & rhs) \ williamr@2: BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) williamr@2: williamr@2: #define BOOST_QUATERNION_OPERATOR_GENERATOR_2_L(op) \ williamr@2: template \ williamr@2: inline quaternion operator op (::std::complex const & lhs, quaternion const & rhs) \ williamr@2: BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) williamr@2: williamr@2: #define BOOST_QUATERNION_OPERATOR_GENERATOR_2_R(op) \ williamr@2: template \ williamr@2: inline quaternion operator op (quaternion const & lhs, ::std::complex const & rhs) \ williamr@2: BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) williamr@2: williamr@2: #define BOOST_QUATERNION_OPERATOR_GENERATOR_3(op) \ williamr@2: template \ williamr@2: inline quaternion operator op (quaternion const & lhs, quaternion const & rhs) \ williamr@2: BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) williamr@2: williamr@2: #define BOOST_QUATERNION_OPERATOR_GENERATOR(op) \ williamr@2: BOOST_QUATERNION_OPERATOR_GENERATOR_1_L(op) \ williamr@2: BOOST_QUATERNION_OPERATOR_GENERATOR_1_R(op) \ williamr@2: BOOST_QUATERNION_OPERATOR_GENERATOR_2_L(op) \ williamr@2: BOOST_QUATERNION_OPERATOR_GENERATOR_2_R(op) \ williamr@2: BOOST_QUATERNION_OPERATOR_GENERATOR_3(op) williamr@2: williamr@2: williamr@2: BOOST_QUATERNION_OPERATOR_GENERATOR(+) williamr@2: BOOST_QUATERNION_OPERATOR_GENERATOR(-) williamr@2: BOOST_QUATERNION_OPERATOR_GENERATOR(*) williamr@2: BOOST_QUATERNION_OPERATOR_GENERATOR(/) williamr@2: williamr@2: williamr@2: #undef BOOST_QUATERNION_OPERATOR_GENERATOR williamr@2: williamr@2: #undef BOOST_QUATERNION_OPERATOR_GENERATOR_1_L williamr@2: #undef BOOST_QUATERNION_OPERATOR_GENERATOR_1_R williamr@2: #undef BOOST_QUATERNION_OPERATOR_GENERATOR_2_L williamr@2: #undef BOOST_QUATERNION_OPERATOR_GENERATOR_2_R williamr@2: #undef BOOST_QUATERNION_OPERATOR_GENERATOR_3 williamr@2: williamr@2: #undef BOOST_QUATERNION_OPERATOR_GENERATOR_BODY williamr@2: williamr@2: williamr@2: template williamr@2: inline quaternion operator + (quaternion const & q) williamr@2: { williamr@2: return(q); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline quaternion operator - (quaternion const & q) williamr@2: { williamr@2: return(quaternion(-q.R_component_1(),-q.R_component_2(),-q.R_component_3(),-q.R_component_4())); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline bool operator == (T const & lhs, quaternion const & rhs) williamr@2: { williamr@2: return ( williamr@2: (rhs.R_component_1() == lhs)&& williamr@2: (rhs.R_component_2() == static_cast(0))&& williamr@2: (rhs.R_component_3() == static_cast(0))&& williamr@2: (rhs.R_component_4() == static_cast(0)) williamr@2: ); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline bool operator == (quaternion const & lhs, T const & rhs) williamr@2: { williamr@2: return ( williamr@2: (lhs.R_component_1() == rhs)&& williamr@2: (lhs.R_component_2() == static_cast(0))&& williamr@2: (lhs.R_component_3() == static_cast(0))&& williamr@2: (lhs.R_component_4() == static_cast(0)) williamr@2: ); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline bool operator == (::std::complex const & lhs, quaternion const & rhs) williamr@2: { williamr@2: return ( williamr@2: (rhs.R_component_1() == lhs.real())&& williamr@2: (rhs.R_component_2() == lhs.imag())&& williamr@2: (rhs.R_component_3() == static_cast(0))&& williamr@2: (rhs.R_component_4() == static_cast(0)) williamr@2: ); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline bool operator == (quaternion const & lhs, ::std::complex const & rhs) williamr@2: { williamr@2: return ( williamr@2: (lhs.R_component_1() == rhs.real())&& williamr@2: (lhs.R_component_2() == rhs.imag())&& williamr@2: (lhs.R_component_3() == static_cast(0))&& williamr@2: (lhs.R_component_4() == static_cast(0)) williamr@2: ); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline bool operator == (quaternion const & lhs, quaternion const & rhs) williamr@2: { williamr@2: return ( williamr@2: (rhs.R_component_1() == lhs.R_component_1())&& williamr@2: (rhs.R_component_2() == lhs.R_component_2())&& williamr@2: (rhs.R_component_3() == lhs.R_component_3())&& williamr@2: (rhs.R_component_4() == lhs.R_component_4()) williamr@2: ); williamr@2: } williamr@2: williamr@2: williamr@2: #define BOOST_QUATERNION_NOT_EQUAL_GENERATOR \ williamr@2: { \ williamr@2: return(!(lhs == rhs)); \ williamr@2: } williamr@2: williamr@2: template williamr@2: inline bool operator != (T const & lhs, quaternion const & rhs) williamr@2: BOOST_QUATERNION_NOT_EQUAL_GENERATOR williamr@2: williamr@2: template williamr@2: inline bool operator != (quaternion const & lhs, T const & rhs) williamr@2: BOOST_QUATERNION_NOT_EQUAL_GENERATOR williamr@2: williamr@2: template williamr@2: inline bool operator != (::std::complex const & lhs, quaternion const & rhs) williamr@2: BOOST_QUATERNION_NOT_EQUAL_GENERATOR williamr@2: williamr@2: template williamr@2: inline bool operator != (quaternion const & lhs, ::std::complex const & rhs) williamr@2: BOOST_QUATERNION_NOT_EQUAL_GENERATOR williamr@2: williamr@2: template williamr@2: inline bool operator != (quaternion const & lhs, quaternion const & rhs) williamr@2: BOOST_QUATERNION_NOT_EQUAL_GENERATOR williamr@2: williamr@2: #undef BOOST_QUATERNION_NOT_EQUAL_GENERATOR williamr@2: williamr@2: williamr@2: // Note: we allow the following formats, whith a, b, c, and d reals williamr@2: // a williamr@2: // (a), (a,b), (a,b,c), (a,b,c,d) williamr@2: // (a,(c)), (a,(c,d)), ((a)), ((a),c), ((a),(c)), ((a),(c,d)), ((a,b)), ((a,b),c), ((a,b),(c)), ((a,b),(c,d)) williamr@2: #if BOOST_WORKAROUND(__GNUC__, < 3) williamr@2: template williamr@2: std::istream & operator >> ( ::std::istream & is, williamr@2: quaternion & q) williamr@2: #else williamr@2: template williamr@2: ::std::basic_istream & operator >> ( ::std::basic_istream & is, williamr@2: quaternion & q) williamr@2: #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ williamr@2: { williamr@2: #if BOOST_WORKAROUND(__GNUC__, < 3) williamr@2: typedef char charT; williamr@2: #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ williamr@2: williamr@2: #ifdef BOOST_NO_STD_LOCALE williamr@2: #else williamr@2: const ::std::ctype & ct = ::std::use_facet< ::std::ctype >(is.getloc()); williamr@2: #endif /* BOOST_NO_STD_LOCALE */ williamr@2: williamr@2: T a = T(); williamr@2: T b = T(); williamr@2: T c = T(); williamr@2: T d = T(); williamr@2: williamr@2: ::std::complex u = ::std::complex(); williamr@2: ::std::complex v = ::std::complex(); williamr@2: williamr@2: charT ch = charT(); williamr@2: char cc; williamr@2: williamr@2: is >> ch; // get the first lexeme williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: #ifdef BOOST_NO_STD_LOCALE williamr@2: cc = ch; williamr@2: #else williamr@2: cc = ct.narrow(ch, char()); williamr@2: #endif /* BOOST_NO_STD_LOCALE */ williamr@2: williamr@2: if (cc == '(') // read "(", possible: (a), (a,b), (a,b,c), (a,b,c,d), (a,(c)), (a,(c,d)), ((a)), ((a),c), ((a),(c)), ((a),(c,d)), ((a,b)), ((a,b),c), ((a,b),(c)), ((a,b,),(c,d,)) williamr@2: { williamr@2: is >> ch; // get the second lexeme williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: #ifdef BOOST_NO_STD_LOCALE williamr@2: cc = ch; williamr@2: #else williamr@2: cc = ct.narrow(ch, char()); williamr@2: #endif /* BOOST_NO_STD_LOCALE */ williamr@2: williamr@2: if (cc == '(') // read "((", possible: ((a)), ((a),c), ((a),(c)), ((a),(c,d)), ((a,b)), ((a,b),c), ((a,b),(c)), ((a,b,),(c,d,)) williamr@2: { williamr@2: is.putback(ch); williamr@2: williamr@2: is >> u; // we extract the first and second components williamr@2: a = u.real(); williamr@2: b = u.imag(); williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: is >> ch; // get the next lexeme williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: #ifdef BOOST_NO_STD_LOCALE williamr@2: cc = ch; williamr@2: #else williamr@2: cc = ct.narrow(ch, char()); williamr@2: #endif /* BOOST_NO_STD_LOCALE */ williamr@2: williamr@2: if (cc == ')') // format: ((a)) or ((a,b)) williamr@2: { williamr@2: q = quaternion(a,b); williamr@2: } williamr@2: else if (cc == ',') // read "((a)," or "((a,b),", possible: ((a),c), ((a),(c)), ((a),(c,d)), ((a,b),c), ((a,b),(c)), ((a,b,),(c,d,)) williamr@2: { williamr@2: is >> v; // we extract the third and fourth components williamr@2: c = v.real(); williamr@2: d = v.imag(); williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: is >> ch; // get the last lexeme williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: #ifdef BOOST_NO_STD_LOCALE williamr@2: cc = ch; williamr@2: #else williamr@2: cc = ct.narrow(ch, char()); williamr@2: #endif /* BOOST_NO_STD_LOCALE */ williamr@2: williamr@2: if (cc == ')') // format: ((a),c), ((a),(c)), ((a),(c,d)), ((a,b),c), ((a,b),(c)) or ((a,b,),(c,d,)) williamr@2: { williamr@2: q = quaternion(a,b,c,d); williamr@2: } williamr@2: else // error williamr@2: { williamr@2: #if BOOST_WORKAROUND(__GNUC__, < 3) williamr@2: is.setstate(::std::ios::failbit); williamr@2: #else williamr@2: is.setstate(::std::ios_base::failbit); williamr@2: #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ williamr@2: } williamr@2: } williamr@2: else // error williamr@2: { williamr@2: #if BOOST_WORKAROUND(__GNUC__, < 3) williamr@2: is.setstate(::std::ios::failbit); williamr@2: #else williamr@2: is.setstate(::std::ios_base::failbit); williamr@2: #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ williamr@2: } williamr@2: } williamr@2: else // read "(a", possible: (a), (a,b), (a,b,c), (a,b,c,d), (a,(c)), (a,(c,d)) williamr@2: { williamr@2: is.putback(ch); williamr@2: williamr@2: is >> a; // we extract the first component williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: is >> ch; // get the third lexeme williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: #ifdef BOOST_NO_STD_LOCALE williamr@2: cc = ch; williamr@2: #else williamr@2: cc = ct.narrow(ch, char()); williamr@2: #endif /* BOOST_NO_STD_LOCALE */ williamr@2: williamr@2: if (cc == ')') // format: (a) williamr@2: { williamr@2: q = quaternion(a); williamr@2: } williamr@2: else if (cc == ',') // read "(a,", possible: (a,b), (a,b,c), (a,b,c,d), (a,(c)), (a,(c,d)) williamr@2: { williamr@2: is >> ch; // get the fourth lexeme williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: #ifdef BOOST_NO_STD_LOCALE williamr@2: cc = ch; williamr@2: #else williamr@2: cc = ct.narrow(ch, char()); williamr@2: #endif /* BOOST_NO_STD_LOCALE */ williamr@2: williamr@2: if (cc == '(') // read "(a,(", possible: (a,(c)), (a,(c,d)) williamr@2: { williamr@2: is.putback(ch); williamr@2: williamr@2: is >> v; // we extract the third and fourth component williamr@2: williamr@2: c = v.real(); williamr@2: d = v.imag(); williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: is >> ch; // get the ninth lexeme williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: #ifdef BOOST_NO_STD_LOCALE williamr@2: cc = ch; williamr@2: #else williamr@2: cc = ct.narrow(ch, char()); williamr@2: #endif /* BOOST_NO_STD_LOCALE */ williamr@2: williamr@2: if (cc == ')') // format: (a,(c)) or (a,(c,d)) williamr@2: { williamr@2: q = quaternion(a,b,c,d); williamr@2: } williamr@2: else // error williamr@2: { williamr@2: #if BOOST_WORKAROUND(__GNUC__, < 3) williamr@2: is.setstate(::std::ios::failbit); williamr@2: #else williamr@2: is.setstate(::std::ios_base::failbit); williamr@2: #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ williamr@2: } williamr@2: } williamr@2: else // read "(a,b", possible: (a,b), (a,b,c), (a,b,c,d) williamr@2: { williamr@2: is.putback(ch); williamr@2: williamr@2: is >> b; // we extract the second component williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: is >> ch; // get the fifth lexeme williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: #ifdef BOOST_NO_STD_LOCALE williamr@2: cc = ch; williamr@2: #else williamr@2: cc = ct.narrow(ch, char()); williamr@2: #endif /* BOOST_NO_STD_LOCALE */ williamr@2: williamr@2: if (cc == ')') // format: (a,b) williamr@2: { williamr@2: q = quaternion(a,b); williamr@2: } williamr@2: else if (cc == ',') // read "(a,b,", possible: (a,b,c), (a,b,c,d) williamr@2: { williamr@2: is >> c; // we extract the third component williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: is >> ch; // get the seventh lexeme williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: #ifdef BOOST_NO_STD_LOCALE williamr@2: cc = ch; williamr@2: #else williamr@2: cc = ct.narrow(ch, char()); williamr@2: #endif /* BOOST_NO_STD_LOCALE */ williamr@2: williamr@2: if (cc == ')') // format: (a,b,c) williamr@2: { williamr@2: q = quaternion(a,b,c); williamr@2: } williamr@2: else if (cc == ',') // read "(a,b,c,", possible: (a,b,c,d) williamr@2: { williamr@2: is >> d; // we extract the fourth component williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: is >> ch; // get the ninth lexeme williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: #ifdef BOOST_NO_STD_LOCALE williamr@2: cc = ch; williamr@2: #else williamr@2: cc = ct.narrow(ch, char()); williamr@2: #endif /* BOOST_NO_STD_LOCALE */ williamr@2: williamr@2: if (cc == ')') // format: (a,b,c,d) williamr@2: { williamr@2: q = quaternion(a,b,c,d); williamr@2: } williamr@2: else // error williamr@2: { williamr@2: #if BOOST_WORKAROUND(__GNUC__, < 3) williamr@2: is.setstate(::std::ios::failbit); williamr@2: #else williamr@2: is.setstate(::std::ios_base::failbit); williamr@2: #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ williamr@2: } williamr@2: } williamr@2: else // error williamr@2: { williamr@2: #if BOOST_WORKAROUND(__GNUC__, < 3) williamr@2: is.setstate(::std::ios::failbit); williamr@2: #else williamr@2: is.setstate(::std::ios_base::failbit); williamr@2: #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ williamr@2: } williamr@2: } williamr@2: else // error williamr@2: { williamr@2: #if BOOST_WORKAROUND(__GNUC__, < 3) williamr@2: is.setstate(::std::ios::failbit); williamr@2: #else williamr@2: is.setstate(::std::ios_base::failbit); williamr@2: #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ williamr@2: } williamr@2: } williamr@2: } williamr@2: else // error williamr@2: { williamr@2: #if BOOST_WORKAROUND(__GNUC__, < 3) williamr@2: is.setstate(::std::ios::failbit); williamr@2: #else williamr@2: is.setstate(::std::ios_base::failbit); williamr@2: #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ williamr@2: } williamr@2: } williamr@2: } williamr@2: else // format: a williamr@2: { williamr@2: is.putback(ch); williamr@2: williamr@2: is >> a; // we extract the first component williamr@2: williamr@2: if (!is.good()) goto finish; williamr@2: williamr@2: q = quaternion(a); williamr@2: } williamr@2: williamr@2: finish: williamr@2: return(is); williamr@2: } williamr@2: williamr@2: williamr@2: #if BOOST_WORKAROUND(__GNUC__, < 3) williamr@2: template williamr@2: ::std::ostream & operator << ( ::std::ostream & os, williamr@2: quaternion const & q) williamr@2: #else williamr@2: template williamr@2: ::std::basic_ostream & operator << ( ::std::basic_ostream & os, williamr@2: quaternion const & q) williamr@2: #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ williamr@2: { williamr@2: #if BOOST_WORKAROUND(__GNUC__, < 3) williamr@2: ::std::ostringstream s; williamr@2: #else williamr@2: ::std::basic_ostringstream s; williamr@2: #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ williamr@2: williamr@2: s.flags(os.flags()); williamr@2: #ifdef BOOST_NO_STD_LOCALE williamr@2: #else williamr@2: s.imbue(os.getloc()); williamr@2: #endif /* BOOST_NO_STD_LOCALE */ williamr@2: s.precision(os.precision()); williamr@2: williamr@2: s << '(' << q.R_component_1() << ',' williamr@2: << q.R_component_2() << ',' williamr@2: << q.R_component_3() << ',' williamr@2: << q.R_component_4() << ')'; williamr@2: williamr@2: return os << s.str(); williamr@2: } williamr@2: williamr@2: williamr@2: // values williamr@2: williamr@2: template williamr@2: inline T real(quaternion const & q) williamr@2: { williamr@2: return(q.real()); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline quaternion unreal(quaternion const & q) williamr@2: { williamr@2: return(q.unreal()); williamr@2: } williamr@2: williamr@2: williamr@2: #define BOOST_QUATERNION_VALARRAY_LOADER \ williamr@2: using ::std::valarray; \ williamr@2: \ williamr@2: valarray temp(4); \ williamr@2: \ williamr@2: temp[0] = q.R_component_1(); \ williamr@2: temp[1] = q.R_component_2(); \ williamr@2: temp[2] = q.R_component_3(); \ williamr@2: temp[3] = q.R_component_4(); williamr@2: williamr@2: williamr@2: template williamr@2: inline T sup(quaternion const & q) williamr@2: { williamr@2: #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP williamr@2: using ::std::abs; williamr@2: #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ williamr@2: williamr@2: BOOST_QUATERNION_VALARRAY_LOADER williamr@2: williamr@2: #if BOOST_WORKAROUND(__GNUC__, < 3) williamr@2: return((BOOST_GET_VALARRAY(T, abs(temp)).max)()); williamr@2: #else williamr@2: return((abs(temp).max)()); williamr@2: #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline T l1(quaternion const & q) williamr@2: { williamr@2: #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP williamr@2: using ::std::abs; williamr@2: #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ williamr@2: williamr@2: BOOST_QUATERNION_VALARRAY_LOADER williamr@2: williamr@2: #if BOOST_WORKAROUND(__GNUC__, < 3) williamr@2: return(BOOST_GET_VALARRAY(T, abs(temp)).sum()); williamr@2: #else williamr@2: return(abs(temp).sum()); williamr@2: #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline T abs(quaternion const & q) williamr@2: { williamr@2: #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP williamr@2: using ::std::abs; williamr@2: #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ williamr@2: williamr@2: using ::std::sqrt; williamr@2: williamr@2: BOOST_QUATERNION_VALARRAY_LOADER williamr@2: williamr@2: #if BOOST_WORKAROUND(__GNUC__, < 3) williamr@2: T maxim = (BOOST_GET_VALARRAY(T, abs(temp)).max)(); // overflow protection williamr@2: #else williamr@2: T maxim = (abs(temp).max)(); // overflow protection williamr@2: #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ williamr@2: williamr@2: if (maxim == static_cast(0)) williamr@2: { williamr@2: return(maxim); williamr@2: } williamr@2: else williamr@2: { williamr@2: T mixam = static_cast(1)/maxim; // prefer multiplications over divisions williamr@2: williamr@2: temp *= mixam; williamr@2: williamr@2: temp *= temp; williamr@2: williamr@2: return(maxim*sqrt(temp.sum())); williamr@2: } williamr@2: williamr@2: //return(sqrt(norm(q))); williamr@2: } williamr@2: williamr@2: williamr@2: #undef BOOST_QUATERNION_VALARRAY_LOADER williamr@2: williamr@2: williamr@2: // Note: This is the Cayley norm, not the Euclidian norm... williamr@2: williamr@2: template williamr@2: inline T norm(quaternionconst & q) williamr@2: { williamr@2: return(real(q*conj(q))); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline quaternion conj(quaternion const & q) williamr@2: { williamr@2: return(quaternion( +q.R_component_1(), williamr@2: -q.R_component_2(), williamr@2: -q.R_component_3(), williamr@2: -q.R_component_4())); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline quaternion spherical( T const & rho, williamr@2: T const & theta, williamr@2: T const & phi1, williamr@2: T const & phi2) williamr@2: { williamr@2: using ::std::cos; williamr@2: using ::std::sin; williamr@2: williamr@2: //T a = cos(theta)*cos(phi1)*cos(phi2); williamr@2: //T b = sin(theta)*cos(phi1)*cos(phi2); williamr@2: //T c = sin(phi1)*cos(phi2); williamr@2: //T d = sin(phi2); williamr@2: williamr@2: T courrant = static_cast(1); williamr@2: williamr@2: T d = sin(phi2); williamr@2: williamr@2: courrant *= cos(phi2); williamr@2: williamr@2: T c = sin(phi1)*courrant; williamr@2: williamr@2: courrant *= cos(phi1); williamr@2: williamr@2: T b = sin(theta)*courrant; williamr@2: T a = cos(theta)*courrant; williamr@2: williamr@2: return(rho*quaternion(a,b,c,d)); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline quaternion semipolar( T const & rho, williamr@2: T const & alpha, williamr@2: T const & theta1, williamr@2: T const & theta2) williamr@2: { williamr@2: using ::std::cos; williamr@2: using ::std::sin; williamr@2: williamr@2: T a = cos(alpha)*cos(theta1); williamr@2: T b = cos(alpha)*sin(theta1); williamr@2: T c = sin(alpha)*cos(theta2); williamr@2: T d = sin(alpha)*sin(theta2); williamr@2: williamr@2: return(rho*quaternion(a,b,c,d)); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline quaternion multipolar( T const & rho1, williamr@2: T const & theta1, williamr@2: T const & rho2, williamr@2: T const & theta2) williamr@2: { williamr@2: using ::std::cos; williamr@2: using ::std::sin; williamr@2: williamr@2: T a = rho1*cos(theta1); williamr@2: T b = rho1*sin(theta1); williamr@2: T c = rho2*cos(theta2); williamr@2: T d = rho2*sin(theta2); williamr@2: williamr@2: return(quaternion(a,b,c,d)); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline quaternion cylindrospherical( T const & t, williamr@2: T const & radius, williamr@2: T const & longitude, williamr@2: T const & latitude) williamr@2: { williamr@2: using ::std::cos; williamr@2: using ::std::sin; williamr@2: williamr@2: williamr@2: williamr@2: T b = radius*cos(longitude)*cos(latitude); williamr@2: T c = radius*sin(longitude)*cos(latitude); williamr@2: T d = radius*sin(latitude); williamr@2: williamr@2: return(quaternion(t,b,c,d)); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline quaternion cylindrical(T const & r, williamr@2: T const & angle, williamr@2: T const & h1, williamr@2: T const & h2) williamr@2: { williamr@2: using ::std::cos; williamr@2: using ::std::sin; williamr@2: williamr@2: T a = r*cos(angle); williamr@2: T b = r*sin(angle); williamr@2: williamr@2: return(quaternion(a,b,h1,h2)); williamr@2: } williamr@2: williamr@2: williamr@2: // transcendentals williamr@2: // (please see the documentation) williamr@2: williamr@2: williamr@2: template williamr@2: inline quaternion exp(quaternion const & q) williamr@2: { williamr@2: using ::std::exp; williamr@2: using ::std::cos; williamr@2: williamr@2: using ::boost::math::sinc_pi; williamr@2: williamr@2: T u = exp(real(q)); williamr@2: williamr@2: T z = abs(unreal(q)); williamr@2: williamr@2: T w = sinc_pi(z); williamr@2: williamr@2: return(u*quaternion(cos(z), williamr@2: w*q.R_component_2(), w*q.R_component_3(), williamr@2: w*q.R_component_4())); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline quaternion cos(quaternion const & q) williamr@2: { williamr@2: using ::std::sin; williamr@2: using ::std::cos; williamr@2: using ::std::cosh; williamr@2: williamr@2: using ::boost::math::sinhc_pi; williamr@2: williamr@2: T z = abs(unreal(q)); williamr@2: williamr@2: T w = -sin(q.real())*sinhc_pi(z); williamr@2: williamr@2: return(quaternion(cos(q.real())*cosh(z), williamr@2: w*q.R_component_2(), w*q.R_component_3(), williamr@2: w*q.R_component_4())); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline quaternion sin(quaternion const & q) williamr@2: { williamr@2: using ::std::sin; williamr@2: using ::std::cos; williamr@2: using ::std::cosh; williamr@2: williamr@2: using ::boost::math::sinhc_pi; williamr@2: williamr@2: T z = abs(unreal(q)); williamr@2: williamr@2: T w = +cos(q.real())*sinhc_pi(z); williamr@2: williamr@2: return(quaternion(sin(q.real())*cosh(z), williamr@2: w*q.R_component_2(), w*q.R_component_3(), williamr@2: w*q.R_component_4())); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline quaternion tan(quaternion const & q) williamr@2: { williamr@2: return(sin(q)/cos(q)); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline quaternion cosh(quaternion const & q) williamr@2: { williamr@2: return((exp(+q)+exp(-q))/static_cast(2)); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline quaternion sinh(quaternion const & q) williamr@2: { williamr@2: return((exp(+q)-exp(-q))/static_cast(2)); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: inline quaternion tanh(quaternion const & q) williamr@2: { williamr@2: return(sinh(q)/cosh(q)); williamr@2: } williamr@2: williamr@2: williamr@2: template williamr@2: quaternion pow(quaternion const & q, williamr@2: int n) williamr@2: { williamr@2: if (n > 1) williamr@2: { williamr@2: int m = n>>1; williamr@2: williamr@2: quaternion result = pow(q, m); williamr@2: williamr@2: result *= result; williamr@2: williamr@2: if (n != (m<<1)) williamr@2: { williamr@2: result *= q; // n odd williamr@2: } williamr@2: williamr@2: return(result); williamr@2: } williamr@2: else if (n == 1) williamr@2: { williamr@2: return(q); williamr@2: } williamr@2: else if (n == 0) williamr@2: { williamr@2: return(quaternion(1)); williamr@2: } williamr@2: else /* n < 0 */ williamr@2: { williamr@2: return(pow(quaternion(1)/q,-n)); williamr@2: } williamr@2: } williamr@2: williamr@2: williamr@2: // helper templates for converting copy constructors (definition) williamr@2: williamr@2: namespace detail williamr@2: { williamr@2: williamr@2: template< typename T, williamr@2: typename U williamr@2: > williamr@2: quaternion quaternion_type_converter(quaternion const & rhs) williamr@2: { williamr@2: return(quaternion( static_cast(rhs.R_component_1()), williamr@2: static_cast(rhs.R_component_2()), williamr@2: static_cast(rhs.R_component_3()), williamr@2: static_cast(rhs.R_component_4()))); williamr@2: } williamr@2: } williamr@2: } williamr@2: } williamr@2: williamr@2: williamr@2: #if BOOST_WORKAROUND(__GNUC__, < 3) williamr@2: #undef BOOST_GET_VALARRAY williamr@2: #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ williamr@2: williamr@2: williamr@2: #endif /* BOOST_QUATERNION_HPP */