Chris@16: // boost quaternion.hpp header file Chris@16: Chris@16: // (C) Copyright Hubert Holin 2001. Chris@16: // Distributed under the Boost Software License, Version 1.0. (See Chris@16: // accompanying file LICENSE_1_0.txt or copy at Chris@16: // http://www.boost.org/LICENSE_1_0.txt) Chris@16: Chris@16: // See http://www.boost.org for updates, documentation, and revision history. Chris@16: Chris@16: #ifndef BOOST_QUATERNION_HPP Chris@16: #define BOOST_QUATERNION_HPP Chris@16: Chris@16: Chris@16: #include Chris@16: #include // for the "<<" and ">>" operators Chris@16: #include // for the "<<" operator Chris@16: Chris@16: #include // for BOOST_NO_STD_LOCALE Chris@16: #include Chris@16: #ifndef BOOST_NO_STD_LOCALE Chris@16: #include // for the "<<" operator Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: #include Chris@16: Chris@16: Chris@16: Chris@16: #include // for the Sinus cardinal Chris@16: #include // for the Hyperbolic Sinus cardinal Chris@16: Chris@16: Chris@16: namespace boost Chris@16: { Chris@16: namespace math Chris@16: { Chris@16: Chris@16: #define BOOST_QUATERNION_ACCESSOR_GENERATOR(type) \ Chris@16: type real() const \ Chris@16: { \ Chris@16: return(a); \ Chris@16: } \ Chris@16: \ Chris@16: quaternion unreal() const \ Chris@16: { \ Chris@16: return(quaternion(static_cast(0),b,c,d)); \ Chris@16: } \ Chris@16: \ Chris@16: type R_component_1() const \ Chris@16: { \ Chris@16: return(a); \ Chris@16: } \ Chris@16: \ Chris@16: type R_component_2() const \ Chris@16: { \ Chris@16: return(b); \ Chris@16: } \ Chris@16: \ Chris@16: type R_component_3() const \ Chris@16: { \ Chris@16: return(c); \ Chris@16: } \ Chris@16: \ Chris@16: type R_component_4() const \ Chris@16: { \ Chris@16: return(d); \ Chris@16: } \ Chris@16: \ Chris@16: ::std::complex C_component_1() const \ Chris@16: { \ Chris@16: return(::std::complex(a,b)); \ Chris@16: } \ Chris@16: \ Chris@16: ::std::complex C_component_2() const \ Chris@16: { \ Chris@16: return(::std::complex(c,d)); \ Chris@16: } Chris@16: Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(type) \ Chris@16: template \ Chris@16: quaternion & operator = (quaternion const & a_affecter) \ Chris@16: { \ Chris@16: a = static_cast(a_affecter.R_component_1()); \ Chris@16: b = static_cast(a_affecter.R_component_2()); \ Chris@16: c = static_cast(a_affecter.R_component_3()); \ Chris@16: d = static_cast(a_affecter.R_component_4()); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } \ Chris@16: \ Chris@16: quaternion & operator = (quaternion const & a_affecter) \ Chris@16: { \ Chris@16: a = a_affecter.a; \ Chris@16: b = a_affecter.b; \ Chris@16: c = a_affecter.c; \ Chris@16: d = a_affecter.d; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } \ Chris@16: \ Chris@16: quaternion & operator = (type const & a_affecter) \ Chris@16: { \ Chris@16: a = a_affecter; \ Chris@16: \ Chris@16: b = c = d = static_cast(0); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } \ Chris@16: \ Chris@16: quaternion & operator = (::std::complex const & a_affecter) \ Chris@16: { \ Chris@16: a = a_affecter.real(); \ Chris@16: b = a_affecter.imag(); \ Chris@16: \ Chris@16: c = d = static_cast(0); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_DATA_GENERATOR(type) \ Chris@16: type a; \ Chris@16: type b; \ Chris@16: type c; \ Chris@16: type d; Chris@16: Chris@16: Chris@16: template Chris@16: class quaternion Chris@16: { Chris@16: public: Chris@16: Chris@16: typedef T value_type; Chris@16: Chris@16: Chris@16: // constructor for H seen as R^4 Chris@16: // (also default constructor) Chris@16: Chris@16: explicit quaternion( T const & requested_a = T(), Chris@16: T const & requested_b = T(), Chris@16: T const & requested_c = T(), Chris@16: T const & requested_d = T()) Chris@16: : a(requested_a), Chris@16: b(requested_b), Chris@16: c(requested_c), Chris@16: d(requested_d) Chris@16: { Chris@16: // nothing to do! Chris@16: } Chris@16: Chris@16: Chris@16: // constructor for H seen as C^2 Chris@16: Chris@16: explicit quaternion( ::std::complex const & z0, Chris@16: ::std::complex const & z1 = ::std::complex()) Chris@16: : a(z0.real()), Chris@16: b(z0.imag()), Chris@16: c(z1.real()), Chris@16: d(z1.imag()) Chris@16: { Chris@16: // nothing to do! Chris@16: } Chris@16: Chris@16: Chris@16: // UNtemplated copy constructor Chris@16: // (this is taken care of by the compiler itself) Chris@16: Chris@16: Chris@16: // templated copy constructor Chris@16: Chris@16: template Chris@16: explicit quaternion(quaternion const & a_recopier) Chris@16: : a(static_cast(a_recopier.R_component_1())), Chris@16: b(static_cast(a_recopier.R_component_2())), Chris@16: c(static_cast(a_recopier.R_component_3())), Chris@16: d(static_cast(a_recopier.R_component_4())) Chris@16: { Chris@16: // nothing to do! Chris@16: } Chris@16: Chris@16: Chris@16: // destructor Chris@16: // (this is taken care of by the compiler itself) Chris@16: Chris@16: Chris@16: // accessors Chris@16: // Chris@16: // Note: Like complex number, quaternions do have a meaningful notion of "real part", Chris@16: // but unlike them there is no meaningful notion of "imaginary part". Chris@16: // Instead there is an "unreal part" which itself is a quaternion, and usually Chris@16: // nothing simpler (as opposed to the complex number case). Chris@16: // However, for practicallity, there are accessors for the other components Chris@16: // (these are necessary for the templated copy constructor, for instance). Chris@16: Chris@16: BOOST_QUATERNION_ACCESSOR_GENERATOR(T) Chris@16: Chris@16: // assignment operators Chris@16: Chris@16: BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(T) Chris@16: Chris@16: // other assignment-related operators Chris@16: // Chris@16: // NOTE: Quaternion multiplication is *NOT* commutative; Chris@16: // symbolically, "q *= rhs;" means "q = q * rhs;" Chris@16: // and "q /= rhs;" means "q = q * inverse_of(rhs);" Chris@16: Chris@16: quaternion & operator += (T const & rhs) Chris@16: { Chris@16: T at = a + rhs; // exception guard Chris@16: Chris@16: a = at; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: quaternion & operator += (::std::complex const & rhs) Chris@16: { Chris@16: T at = a + rhs.real(); // exception guard Chris@16: T bt = b + rhs.imag(); // exception guard Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: quaternion & operator += (quaternion const & rhs) Chris@16: { Chris@16: T at = a + static_cast(rhs.R_component_1()); // exception guard Chris@16: T bt = b + static_cast(rhs.R_component_2()); // exception guard Chris@16: T ct = c + static_cast(rhs.R_component_3()); // exception guard Chris@16: T dt = d + static_cast(rhs.R_component_4()); // exception guard Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: Chris@16: quaternion & operator -= (T const & rhs) Chris@16: { Chris@16: T at = a - rhs; // exception guard Chris@16: Chris@16: a = at; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: quaternion & operator -= (::std::complex const & rhs) Chris@16: { Chris@16: T at = a - rhs.real(); // exception guard Chris@16: T bt = b - rhs.imag(); // exception guard Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: quaternion & operator -= (quaternion const & rhs) Chris@16: { Chris@16: T at = a - static_cast(rhs.R_component_1()); // exception guard Chris@16: T bt = b - static_cast(rhs.R_component_2()); // exception guard Chris@16: T ct = c - static_cast(rhs.R_component_3()); // exception guard Chris@16: T dt = d - static_cast(rhs.R_component_4()); // exception guard Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: quaternion & operator *= (T const & rhs) Chris@16: { Chris@16: T at = a * rhs; // exception guard Chris@16: T bt = b * rhs; // exception guard Chris@16: T ct = c * rhs; // exception guard Chris@16: T dt = d * rhs; // exception guard Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: quaternion & operator *= (::std::complex const & rhs) Chris@16: { Chris@16: T ar = rhs.real(); Chris@16: T br = rhs.imag(); Chris@16: Chris@16: T at = +a*ar-b*br; Chris@16: T bt = +a*br+b*ar; Chris@16: T ct = +c*ar+d*br; Chris@16: T dt = -c*br+d*ar; Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: quaternion & operator *= (quaternion const & rhs) Chris@16: { Chris@16: T ar = static_cast(rhs.R_component_1()); Chris@16: T br = static_cast(rhs.R_component_2()); Chris@16: T cr = static_cast(rhs.R_component_3()); Chris@16: T dr = static_cast(rhs.R_component_4()); Chris@16: Chris@16: T at = +a*ar-b*br-c*cr-d*dr; Chris@16: T bt = +a*br+b*ar+c*dr-d*cr; //(a*br+ar*b)+(c*dr-cr*d); Chris@16: T ct = +a*cr-b*dr+c*ar+d*br; //(a*cr+ar*c)+(d*br-dr*b); Chris@16: T dt = +a*dr+b*cr-c*br+d*ar; //(a*dr+ar*d)+(b*cr-br*c); Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: Chris@16: quaternion & operator /= (T const & rhs) Chris@16: { Chris@16: T at = a / rhs; // exception guard Chris@16: T bt = b / rhs; // exception guard Chris@16: T ct = c / rhs; // exception guard Chris@16: T dt = d / rhs; // exception guard Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: quaternion & operator /= (::std::complex const & rhs) Chris@16: { Chris@16: T ar = rhs.real(); Chris@16: T br = rhs.imag(); Chris@16: Chris@16: T denominator = ar*ar+br*br; Chris@16: Chris@16: T at = (+a*ar+b*br)/denominator; //(a*ar+b*br)/denominator; Chris@16: T bt = (-a*br+b*ar)/denominator; //(ar*b-a*br)/denominator; Chris@16: T ct = (+c*ar-d*br)/denominator; //(ar*c-d*br)/denominator; Chris@16: T dt = (+c*br+d*ar)/denominator; //(ar*d+br*c)/denominator; Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: quaternion & operator /= (quaternion const & rhs) Chris@16: { Chris@16: T ar = static_cast(rhs.R_component_1()); Chris@16: T br = static_cast(rhs.R_component_2()); Chris@16: T cr = static_cast(rhs.R_component_3()); Chris@16: T dr = static_cast(rhs.R_component_4()); Chris@16: Chris@16: T denominator = ar*ar+br*br+cr*cr+dr*dr; Chris@16: Chris@16: T at = (+a*ar+b*br+c*cr+d*dr)/denominator; //(a*ar+b*br+c*cr+d*dr)/denominator; Chris@16: T bt = (-a*br+b*ar-c*dr+d*cr)/denominator; //((ar*b-a*br)+(cr*d-c*dr))/denominator; Chris@16: T ct = (-a*cr+b*dr+c*ar-d*br)/denominator; //((ar*c-a*cr)+(dr*b-d*br))/denominator; Chris@16: T dt = (-a*dr-b*cr+c*br+d*ar)/denominator; //((ar*d-a*dr)+(br*c-b*cr))/denominator; Chris@16: Chris@16: a = at; Chris@16: b = bt; Chris@16: c = ct; Chris@16: d = dt; Chris@16: Chris@16: return(*this); Chris@16: } Chris@16: Chris@16: Chris@16: protected: Chris@16: Chris@16: BOOST_QUATERNION_MEMBER_DATA_GENERATOR(T) Chris@16: Chris@16: Chris@16: private: Chris@16: Chris@16: }; Chris@16: Chris@16: Chris@16: // declaration of quaternion specialization Chris@16: Chris@16: template<> class quaternion; Chris@16: template<> class quaternion; Chris@16: template<> class quaternion; Chris@16: Chris@16: Chris@16: // helper templates for converting copy constructors (declaration) Chris@16: Chris@16: namespace detail Chris@16: { Chris@16: Chris@16: template< typename T, Chris@16: typename U Chris@16: > Chris@16: quaternion quaternion_type_converter(quaternion const & rhs); Chris@16: } Chris@16: Chris@16: Chris@16: // implementation of quaternion specialization Chris@16: Chris@16: Chris@16: #define BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(type) \ Chris@16: explicit quaternion( type const & requested_a = static_cast(0), \ Chris@16: type const & requested_b = static_cast(0), \ Chris@16: type const & requested_c = static_cast(0), \ Chris@16: type const & requested_d = static_cast(0)) \ Chris@16: : a(requested_a), \ Chris@16: b(requested_b), \ Chris@16: c(requested_c), \ Chris@16: d(requested_d) \ Chris@16: { \ Chris@16: } \ Chris@16: \ Chris@16: explicit quaternion( ::std::complex const & z0, \ Chris@16: ::std::complex const & z1 = ::std::complex()) \ Chris@16: : a(z0.real()), \ Chris@16: b(z0.imag()), \ Chris@16: c(z1.real()), \ Chris@16: d(z1.imag()) \ Chris@16: { \ Chris@16: } Chris@16: Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_ADD_GENERATOR_1(type) \ Chris@16: quaternion & operator += (type const & rhs) \ Chris@16: { \ Chris@16: a += rhs; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_ADD_GENERATOR_2(type) \ Chris@16: quaternion & operator += (::std::complex const & rhs) \ Chris@16: { \ Chris@16: a += rhs.real(); \ Chris@16: b += rhs.imag(); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_ADD_GENERATOR_3(type) \ Chris@16: template \ Chris@16: quaternion & operator += (quaternion const & rhs) \ Chris@16: { \ Chris@16: a += static_cast(rhs.R_component_1()); \ Chris@16: b += static_cast(rhs.R_component_2()); \ Chris@16: c += static_cast(rhs.R_component_3()); \ Chris@16: d += static_cast(rhs.R_component_4()); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_SUB_GENERATOR_1(type) \ Chris@16: quaternion & operator -= (type const & rhs) \ Chris@16: { \ Chris@16: a -= rhs; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_SUB_GENERATOR_2(type) \ Chris@16: quaternion & operator -= (::std::complex const & rhs) \ Chris@16: { \ Chris@16: a -= rhs.real(); \ Chris@16: b -= rhs.imag(); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_SUB_GENERATOR_3(type) \ Chris@16: template \ Chris@16: quaternion & operator -= (quaternion const & rhs) \ Chris@16: { \ Chris@16: a -= static_cast(rhs.R_component_1()); \ Chris@16: b -= static_cast(rhs.R_component_2()); \ Chris@16: c -= static_cast(rhs.R_component_3()); \ Chris@16: d -= static_cast(rhs.R_component_4()); \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_MUL_GENERATOR_1(type) \ Chris@16: quaternion & operator *= (type const & rhs) \ Chris@16: { \ Chris@16: a *= rhs; \ Chris@16: b *= rhs; \ Chris@16: c *= rhs; \ Chris@16: d *= rhs; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_MUL_GENERATOR_2(type) \ Chris@16: quaternion & operator *= (::std::complex const & rhs) \ Chris@16: { \ Chris@16: type ar = rhs.real(); \ Chris@16: type br = rhs.imag(); \ Chris@16: \ Chris@16: type at = +a*ar-b*br; \ Chris@16: type bt = +a*br+b*ar; \ Chris@16: type ct = +c*ar+d*br; \ Chris@16: type dt = -c*br+d*ar; \ Chris@16: \ Chris@16: a = at; \ Chris@16: b = bt; \ Chris@16: c = ct; \ Chris@16: d = dt; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_MUL_GENERATOR_3(type) \ Chris@16: template \ Chris@16: quaternion & operator *= (quaternion const & rhs) \ Chris@16: { \ Chris@16: type ar = static_cast(rhs.R_component_1()); \ Chris@16: type br = static_cast(rhs.R_component_2()); \ Chris@16: type cr = static_cast(rhs.R_component_3()); \ Chris@16: type dr = static_cast(rhs.R_component_4()); \ Chris@16: \ Chris@16: type at = +a*ar-b*br-c*cr-d*dr; \ Chris@16: type bt = +a*br+b*ar+c*dr-d*cr; \ Chris@16: type ct = +a*cr-b*dr+c*ar+d*br; \ Chris@16: type dt = +a*dr+b*cr-c*br+d*ar; \ Chris@16: \ Chris@16: a = at; \ Chris@16: b = bt; \ Chris@16: c = ct; \ Chris@16: d = dt; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@16: // There is quite a lot of repetition in the code below. This is intentional. Chris@16: // The last conditional block is the normal form, and the others merely Chris@16: // consist of workarounds for various compiler deficiencies. Hopefuly, when Chris@16: // more compilers are conformant and we can retire support for those that are Chris@16: // not, we will be able to remove the clutter. This is makes the situation Chris@16: // (painfully) explicit. Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_1(type) \ Chris@16: quaternion & operator /= (type const & rhs) \ Chris@16: { \ Chris@16: a /= rhs; \ Chris@16: b /= rhs; \ Chris@16: c /= rhs; \ Chris@16: d /= rhs; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: Chris@101: #if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) Chris@16: #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \ Chris@16: quaternion & operator /= (::std::complex const & rhs) \ Chris@16: { \ Chris@16: using ::std::valarray; \ Chris@16: using ::std::abs; \ Chris@16: \ Chris@16: valarray tr(2); \ Chris@16: \ Chris@16: tr[0] = rhs.real(); \ Chris@16: tr[1] = rhs.imag(); \ Chris@16: \ Chris@16: type mixam = static_cast(1)/(abs(tr).max)(); \ Chris@16: \ Chris@16: tr *= mixam; \ Chris@16: \ Chris@16: valarray tt(4); \ Chris@16: \ Chris@16: tt[0] = +a*tr[0]+b*tr[1]; \ Chris@16: tt[1] = -a*tr[1]+b*tr[0]; \ Chris@16: tt[2] = +c*tr[0]-d*tr[1]; \ Chris@16: tt[3] = +c*tr[1]+d*tr[0]; \ Chris@16: \ Chris@16: tr *= tr; \ Chris@16: \ Chris@16: tt *= (mixam/tr.sum()); \ Chris@16: \ Chris@16: a = tt[0]; \ Chris@16: b = tt[1]; \ Chris@16: c = tt[2]; \ Chris@16: d = tt[3]; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: #else Chris@16: #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \ Chris@16: quaternion & operator /= (::std::complex const & rhs) \ Chris@16: { \ Chris@16: using ::std::valarray; \ Chris@16: \ Chris@16: valarray tr(2); \ Chris@16: \ Chris@16: tr[0] = rhs.real(); \ Chris@16: tr[1] = rhs.imag(); \ Chris@16: \ Chris@16: type mixam = static_cast(1)/(abs(tr).max)(); \ Chris@16: \ Chris@16: tr *= mixam; \ Chris@16: \ Chris@16: valarray tt(4); \ Chris@16: \ Chris@16: tt[0] = +a*tr[0]+b*tr[1]; \ Chris@16: tt[1] = -a*tr[1]+b*tr[0]; \ Chris@16: tt[2] = +c*tr[0]-d*tr[1]; \ Chris@16: tt[3] = +c*tr[1]+d*tr[0]; \ Chris@16: \ Chris@16: tr *= tr; \ Chris@16: \ Chris@16: tt *= (mixam/tr.sum()); \ Chris@16: \ Chris@16: a = tt[0]; \ Chris@16: b = tt[1]; \ Chris@16: c = tt[2]; \ Chris@16: d = tt[3]; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@101: #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ Chris@16: Chris@101: #if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) Chris@16: #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type) \ Chris@16: template \ Chris@16: quaternion & operator /= (quaternion const & rhs) \ Chris@16: { \ Chris@16: using ::std::valarray; \ Chris@16: using ::std::abs; \ Chris@16: \ Chris@16: valarray tr(4); \ Chris@16: \ Chris@16: tr[0] = static_cast(rhs.R_component_1()); \ Chris@16: tr[1] = static_cast(rhs.R_component_2()); \ Chris@16: tr[2] = static_cast(rhs.R_component_3()); \ Chris@16: tr[3] = static_cast(rhs.R_component_4()); \ Chris@16: \ Chris@16: type mixam = static_cast(1)/(abs(tr).max)(); \ Chris@16: \ Chris@16: tr *= mixam; \ Chris@16: \ Chris@16: valarray tt(4); \ Chris@16: \ Chris@16: tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \ Chris@16: tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \ Chris@16: tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \ Chris@16: tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \ Chris@16: \ Chris@16: tr *= tr; \ Chris@16: \ Chris@16: tt *= (mixam/tr.sum()); \ Chris@16: \ Chris@16: a = tt[0]; \ Chris@16: b = tt[1]; \ Chris@16: c = tt[2]; \ Chris@16: d = tt[3]; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@16: #else Chris@16: #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type) \ Chris@16: template \ Chris@16: quaternion & operator /= (quaternion const & rhs) \ Chris@16: { \ Chris@16: using ::std::valarray; \ Chris@16: \ Chris@16: valarray tr(4); \ Chris@16: \ Chris@16: tr[0] = static_cast(rhs.R_component_1()); \ Chris@16: tr[1] = static_cast(rhs.R_component_2()); \ Chris@16: tr[2] = static_cast(rhs.R_component_3()); \ Chris@16: tr[3] = static_cast(rhs.R_component_4()); \ Chris@16: \ Chris@16: type mixam = static_cast(1)/(abs(tr).max)(); \ Chris@16: \ Chris@16: tr *= mixam; \ Chris@16: \ Chris@16: valarray tt(4); \ Chris@16: \ Chris@16: tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \ Chris@16: tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \ Chris@16: tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \ Chris@16: tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \ Chris@16: \ Chris@16: tr *= tr; \ Chris@16: \ Chris@16: tt *= (mixam/tr.sum()); \ Chris@16: \ Chris@16: a = tt[0]; \ Chris@16: b = tt[1]; \ Chris@16: c = tt[2]; \ Chris@16: d = tt[3]; \ Chris@16: \ Chris@16: return(*this); \ Chris@16: } Chris@101: #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_ADD_GENERATOR(type) \ Chris@16: BOOST_QUATERNION_MEMBER_ADD_GENERATOR_1(type) \ Chris@16: BOOST_QUATERNION_MEMBER_ADD_GENERATOR_2(type) \ Chris@16: BOOST_QUATERNION_MEMBER_ADD_GENERATOR_3(type) Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_SUB_GENERATOR(type) \ Chris@16: BOOST_QUATERNION_MEMBER_SUB_GENERATOR_1(type) \ Chris@16: BOOST_QUATERNION_MEMBER_SUB_GENERATOR_2(type) \ Chris@16: BOOST_QUATERNION_MEMBER_SUB_GENERATOR_3(type) Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_MUL_GENERATOR(type) \ Chris@16: BOOST_QUATERNION_MEMBER_MUL_GENERATOR_1(type) \ Chris@16: BOOST_QUATERNION_MEMBER_MUL_GENERATOR_2(type) \ Chris@16: BOOST_QUATERNION_MEMBER_MUL_GENERATOR_3(type) Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR(type) \ Chris@16: BOOST_QUATERNION_MEMBER_DIV_GENERATOR_1(type) \ Chris@16: BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \ Chris@16: BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type) Chris@16: Chris@16: #define BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(type) \ Chris@16: BOOST_QUATERNION_MEMBER_ADD_GENERATOR(type) \ Chris@16: BOOST_QUATERNION_MEMBER_SUB_GENERATOR(type) \ Chris@16: BOOST_QUATERNION_MEMBER_MUL_GENERATOR(type) \ Chris@16: BOOST_QUATERNION_MEMBER_DIV_GENERATOR(type) Chris@16: Chris@16: Chris@16: template<> Chris@16: class quaternion Chris@16: { Chris@16: public: Chris@16: Chris@16: typedef float value_type; Chris@16: Chris@16: BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(float) Chris@16: Chris@16: // UNtemplated copy constructor Chris@16: // (this is taken care of by the compiler itself) Chris@16: Chris@16: // explicit copy constructors (precision-loosing converters) Chris@16: Chris@16: explicit quaternion(quaternion const & a_recopier) Chris@16: { Chris@16: *this = detail::quaternion_type_converter(a_recopier); Chris@16: } Chris@16: Chris@16: explicit quaternion(quaternion const & a_recopier) Chris@16: { Chris@16: *this = detail::quaternion_type_converter(a_recopier); Chris@16: } Chris@16: Chris@16: // destructor Chris@16: // (this is taken care of by the compiler itself) Chris@16: Chris@16: // accessors Chris@16: // Chris@16: // Note: Like complex number, quaternions do have a meaningful notion of "real part", Chris@16: // but unlike them there is no meaningful notion of "imaginary part". Chris@16: // Instead there is an "unreal part" which itself is a quaternion, and usually Chris@16: // nothing simpler (as opposed to the complex number case). Chris@16: // However, for practicallity, there are accessors for the other components Chris@16: // (these are necessary for the templated copy constructor, for instance). Chris@16: Chris@16: BOOST_QUATERNION_ACCESSOR_GENERATOR(float) Chris@16: Chris@16: // assignment operators Chris@16: Chris@16: BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(float) Chris@16: Chris@16: // other assignment-related operators Chris@16: // Chris@16: // NOTE: Quaternion multiplication is *NOT* commutative; Chris@16: // symbolically, "q *= rhs;" means "q = q * rhs;" Chris@16: // and "q /= rhs;" means "q = q * inverse_of(rhs);" Chris@16: Chris@16: BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(float) Chris@16: Chris@16: Chris@16: protected: Chris@16: Chris@16: BOOST_QUATERNION_MEMBER_DATA_GENERATOR(float) Chris@16: Chris@16: Chris@16: private: Chris@16: Chris@16: }; Chris@16: Chris@16: Chris@16: template<> Chris@16: class quaternion Chris@16: { Chris@16: public: Chris@16: Chris@16: typedef double value_type; Chris@16: Chris@16: BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(double) Chris@16: Chris@16: // UNtemplated copy constructor Chris@16: // (this is taken care of by the compiler itself) Chris@16: Chris@16: // converting copy constructor Chris@16: Chris@16: explicit quaternion(quaternion const & a_recopier) Chris@16: { Chris@16: *this = detail::quaternion_type_converter(a_recopier); Chris@16: } Chris@16: Chris@16: // explicit copy constructors (precision-loosing converters) Chris@16: Chris@16: explicit quaternion(quaternion const & a_recopier) Chris@16: { Chris@16: *this = detail::quaternion_type_converter(a_recopier); Chris@16: } Chris@16: Chris@16: // destructor Chris@16: // (this is taken care of by the compiler itself) Chris@16: Chris@16: // accessors Chris@16: // Chris@16: // Note: Like complex number, quaternions do have a meaningful notion of "real part", Chris@16: // but unlike them there is no meaningful notion of "imaginary part". Chris@16: // Instead there is an "unreal part" which itself is a quaternion, and usually Chris@16: // nothing simpler (as opposed to the complex number case). Chris@16: // However, for practicallity, there are accessors for the other components Chris@16: // (these are necessary for the templated copy constructor, for instance). Chris@16: Chris@16: BOOST_QUATERNION_ACCESSOR_GENERATOR(double) Chris@16: Chris@16: // assignment operators Chris@16: Chris@16: BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(double) Chris@16: Chris@16: // other assignment-related operators Chris@16: // Chris@16: // NOTE: Quaternion multiplication is *NOT* commutative; Chris@16: // symbolically, "q *= rhs;" means "q = q * rhs;" Chris@16: // and "q /= rhs;" means "q = q * inverse_of(rhs);" Chris@16: Chris@16: BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(double) Chris@16: Chris@16: Chris@16: protected: Chris@16: Chris@16: BOOST_QUATERNION_MEMBER_DATA_GENERATOR(double) Chris@16: Chris@16: Chris@16: private: Chris@16: Chris@16: }; Chris@16: Chris@16: Chris@16: template<> Chris@16: class quaternion Chris@16: { Chris@16: public: Chris@16: Chris@16: typedef long double value_type; Chris@16: Chris@16: BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(long double) Chris@16: Chris@16: // UNtemplated copy constructor Chris@16: // (this is taken care of by the compiler itself) Chris@16: Chris@16: // converting copy constructors Chris@16: Chris@16: explicit quaternion(quaternion const & a_recopier) Chris@16: { Chris@16: *this = detail::quaternion_type_converter(a_recopier); Chris@16: } Chris@16: Chris@16: explicit quaternion(quaternion const & a_recopier) Chris@16: { Chris@16: *this = detail::quaternion_type_converter(a_recopier); Chris@16: } Chris@16: Chris@16: // destructor Chris@16: // (this is taken care of by the compiler itself) Chris@16: Chris@16: // accessors Chris@16: // Chris@16: // Note: Like complex number, quaternions do have a meaningful notion of "real part", Chris@16: // but unlike them there is no meaningful notion of "imaginary part". Chris@16: // Instead there is an "unreal part" which itself is a quaternion, and usually Chris@16: // nothing simpler (as opposed to the complex number case). Chris@16: // However, for practicallity, there are accessors for the other components Chris@16: // (these are necessary for the templated copy constructor, for instance). Chris@16: Chris@16: BOOST_QUATERNION_ACCESSOR_GENERATOR(long double) Chris@16: Chris@16: // assignment operators Chris@16: Chris@16: BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(long double) Chris@16: Chris@16: // other assignment-related operators Chris@16: // Chris@16: // NOTE: Quaternion multiplication is *NOT* commutative; Chris@16: // symbolically, "q *= rhs;" means "q = q * rhs;" Chris@16: // and "q /= rhs;" means "q = q * inverse_of(rhs);" Chris@16: Chris@16: BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(long double) Chris@16: Chris@16: Chris@16: protected: Chris@16: Chris@16: BOOST_QUATERNION_MEMBER_DATA_GENERATOR(long double) Chris@16: Chris@16: Chris@16: private: Chris@16: Chris@16: }; Chris@16: Chris@16: Chris@16: #undef BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR Chris@16: #undef BOOST_QUATERNION_MEMBER_ADD_GENERATOR Chris@16: #undef BOOST_QUATERNION_MEMBER_SUB_GENERATOR Chris@16: #undef BOOST_QUATERNION_MEMBER_MUL_GENERATOR Chris@16: #undef BOOST_QUATERNION_MEMBER_DIV_GENERATOR Chris@16: #undef BOOST_QUATERNION_MEMBER_ADD_GENERATOR_1 Chris@16: #undef BOOST_QUATERNION_MEMBER_ADD_GENERATOR_2 Chris@16: #undef BOOST_QUATERNION_MEMBER_ADD_GENERATOR_3 Chris@16: #undef BOOST_QUATERNION_MEMBER_SUB_GENERATOR_1 Chris@16: #undef BOOST_QUATERNION_MEMBER_SUB_GENERATOR_2 Chris@16: #undef BOOST_QUATERNION_MEMBER_SUB_GENERATOR_3 Chris@16: #undef BOOST_QUATERNION_MEMBER_MUL_GENERATOR_1 Chris@16: #undef BOOST_QUATERNION_MEMBER_MUL_GENERATOR_2 Chris@16: #undef BOOST_QUATERNION_MEMBER_MUL_GENERATOR_3 Chris@16: #undef BOOST_QUATERNION_MEMBER_DIV_GENERATOR_1 Chris@16: #undef BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2 Chris@16: #undef BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3 Chris@16: Chris@16: #undef BOOST_QUATERNION_CONSTRUCTOR_GENERATOR Chris@16: Chris@16: Chris@16: #undef BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR Chris@16: Chris@16: #undef BOOST_QUATERNION_MEMBER_DATA_GENERATOR Chris@16: Chris@16: #undef BOOST_QUATERNION_ACCESSOR_GENERATOR Chris@16: Chris@16: Chris@16: // operators Chris@16: Chris@16: #define BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) \ Chris@16: { \ Chris@16: quaternion res(lhs); \ Chris@16: res op##= rhs; \ Chris@16: return(res); \ Chris@16: } Chris@16: Chris@16: #define BOOST_QUATERNION_OPERATOR_GENERATOR_1_L(op) \ Chris@16: template \ Chris@16: inline quaternion operator op (T const & lhs, quaternion const & rhs) \ Chris@16: BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) Chris@16: Chris@16: #define BOOST_QUATERNION_OPERATOR_GENERATOR_1_R(op) \ Chris@16: template \ Chris@16: inline quaternion operator op (quaternion const & lhs, T const & rhs) \ Chris@16: BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) Chris@16: Chris@16: #define BOOST_QUATERNION_OPERATOR_GENERATOR_2_L(op) \ Chris@16: template \ Chris@16: inline quaternion operator op (::std::complex const & lhs, quaternion const & rhs) \ Chris@16: BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) Chris@16: Chris@16: #define BOOST_QUATERNION_OPERATOR_GENERATOR_2_R(op) \ Chris@16: template \ Chris@16: inline quaternion operator op (quaternion const & lhs, ::std::complex const & rhs) \ Chris@16: BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) Chris@16: Chris@16: #define BOOST_QUATERNION_OPERATOR_GENERATOR_3(op) \ Chris@16: template \ Chris@16: inline quaternion operator op (quaternion const & lhs, quaternion const & rhs) \ Chris@16: BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) Chris@16: Chris@16: #define BOOST_QUATERNION_OPERATOR_GENERATOR(op) \ Chris@16: BOOST_QUATERNION_OPERATOR_GENERATOR_1_L(op) \ Chris@16: BOOST_QUATERNION_OPERATOR_GENERATOR_1_R(op) \ Chris@16: BOOST_QUATERNION_OPERATOR_GENERATOR_2_L(op) \ Chris@16: BOOST_QUATERNION_OPERATOR_GENERATOR_2_R(op) \ Chris@16: BOOST_QUATERNION_OPERATOR_GENERATOR_3(op) Chris@16: Chris@16: Chris@16: BOOST_QUATERNION_OPERATOR_GENERATOR(+) Chris@16: BOOST_QUATERNION_OPERATOR_GENERATOR(-) Chris@16: BOOST_QUATERNION_OPERATOR_GENERATOR(*) Chris@16: BOOST_QUATERNION_OPERATOR_GENERATOR(/) Chris@16: Chris@16: Chris@16: #undef BOOST_QUATERNION_OPERATOR_GENERATOR Chris@16: Chris@16: #undef BOOST_QUATERNION_OPERATOR_GENERATOR_1_L Chris@16: #undef BOOST_QUATERNION_OPERATOR_GENERATOR_1_R Chris@16: #undef BOOST_QUATERNION_OPERATOR_GENERATOR_2_L Chris@16: #undef BOOST_QUATERNION_OPERATOR_GENERATOR_2_R Chris@16: #undef BOOST_QUATERNION_OPERATOR_GENERATOR_3 Chris@16: Chris@16: #undef BOOST_QUATERNION_OPERATOR_GENERATOR_BODY Chris@16: Chris@16: Chris@16: template Chris@16: inline quaternion operator + (quaternion const & q) Chris@16: { Chris@16: return(q); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline quaternion operator - (quaternion const & q) Chris@16: { Chris@16: return(quaternion(-q.R_component_1(),-q.R_component_2(),-q.R_component_3(),-q.R_component_4())); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline bool operator == (T const & lhs, quaternion const & rhs) Chris@16: { Chris@16: return ( Chris@16: (rhs.R_component_1() == lhs)&& Chris@16: (rhs.R_component_2() == static_cast(0))&& Chris@16: (rhs.R_component_3() == static_cast(0))&& Chris@16: (rhs.R_component_4() == static_cast(0)) Chris@16: ); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline bool operator == (quaternion const & lhs, T const & rhs) Chris@16: { Chris@16: return ( Chris@16: (lhs.R_component_1() == rhs)&& Chris@16: (lhs.R_component_2() == static_cast(0))&& Chris@16: (lhs.R_component_3() == static_cast(0))&& Chris@16: (lhs.R_component_4() == static_cast(0)) Chris@16: ); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline bool operator == (::std::complex const & lhs, quaternion const & rhs) Chris@16: { Chris@16: return ( Chris@16: (rhs.R_component_1() == lhs.real())&& Chris@16: (rhs.R_component_2() == lhs.imag())&& Chris@16: (rhs.R_component_3() == static_cast(0))&& Chris@16: (rhs.R_component_4() == static_cast(0)) Chris@16: ); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline bool operator == (quaternion const & lhs, ::std::complex const & rhs) Chris@16: { Chris@16: return ( Chris@16: (lhs.R_component_1() == rhs.real())&& Chris@16: (lhs.R_component_2() == rhs.imag())&& Chris@16: (lhs.R_component_3() == static_cast(0))&& Chris@16: (lhs.R_component_4() == static_cast(0)) Chris@16: ); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline bool operator == (quaternion const & lhs, quaternion const & rhs) Chris@16: { Chris@16: return ( Chris@16: (rhs.R_component_1() == lhs.R_component_1())&& Chris@16: (rhs.R_component_2() == lhs.R_component_2())&& Chris@16: (rhs.R_component_3() == lhs.R_component_3())&& Chris@16: (rhs.R_component_4() == lhs.R_component_4()) Chris@16: ); Chris@16: } Chris@16: Chris@16: Chris@16: #define BOOST_QUATERNION_NOT_EQUAL_GENERATOR \ Chris@16: { \ Chris@16: return(!(lhs == rhs)); \ Chris@16: } Chris@16: Chris@16: template Chris@16: inline bool operator != (T const & lhs, quaternion const & rhs) Chris@16: BOOST_QUATERNION_NOT_EQUAL_GENERATOR Chris@16: Chris@16: template Chris@16: inline bool operator != (quaternion const & lhs, T const & rhs) Chris@16: BOOST_QUATERNION_NOT_EQUAL_GENERATOR Chris@16: Chris@16: template Chris@16: inline bool operator != (::std::complex const & lhs, quaternion const & rhs) Chris@16: BOOST_QUATERNION_NOT_EQUAL_GENERATOR Chris@16: Chris@16: template Chris@16: inline bool operator != (quaternion const & lhs, ::std::complex const & rhs) Chris@16: BOOST_QUATERNION_NOT_EQUAL_GENERATOR Chris@16: Chris@16: template Chris@16: inline bool operator != (quaternion const & lhs, quaternion const & rhs) Chris@16: BOOST_QUATERNION_NOT_EQUAL_GENERATOR Chris@16: Chris@16: #undef BOOST_QUATERNION_NOT_EQUAL_GENERATOR Chris@16: Chris@16: Chris@16: // Note: we allow the following formats, whith a, b, c, and d reals Chris@16: // a Chris@16: // (a), (a,b), (a,b,c), (a,b,c,d) Chris@16: // (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)) Chris@16: template Chris@16: ::std::basic_istream & operator >> ( ::std::basic_istream & is, Chris@16: quaternion & q) Chris@16: { Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: #else Chris@16: const ::std::ctype & ct = ::std::use_facet< ::std::ctype >(is.getloc()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: T a = T(); Chris@16: T b = T(); Chris@16: T c = T(); Chris@16: T d = T(); Chris@16: Chris@16: ::std::complex u = ::std::complex(); Chris@16: ::std::complex v = ::std::complex(); Chris@16: Chris@16: charT ch = charT(); Chris@16: char cc; Chris@16: Chris@16: is >> ch; // get the first lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: 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,)) Chris@16: { Chris@16: is >> ch; // get the second lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "((", possible: ((a)), ((a),c), ((a),(c)), ((a),(c,d)), ((a,b)), ((a,b),c), ((a,b),(c)), ((a,b,),(c,d,)) Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> u; // we extract the first and second components Chris@16: a = u.real(); Chris@16: b = u.imag(); Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the next lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // format: ((a)) or ((a,b)) Chris@16: { Chris@16: q = quaternion(a,b); Chris@16: } Chris@16: 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,)) Chris@16: { Chris@16: is >> v; // we extract the third and fourth components Chris@16: c = v.real(); Chris@16: d = v.imag(); Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the last lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // format: ((a),c), ((a),(c)), ((a),(c,d)), ((a,b),c), ((a,b),(c)) or ((a,b,),(c,d,)) Chris@16: { Chris@16: q = quaternion(a,b,c,d); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // read "(a", possible: (a), (a,b), (a,b,c), (a,b,c,d), (a,(c)), (a,(c,d)) Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> a; // we extract the first component Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the third lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // format: (a) Chris@16: { Chris@16: q = quaternion(a); Chris@16: } Chris@16: else if (cc == ',') // read "(a,", possible: (a,b), (a,b,c), (a,b,c,d), (a,(c)), (a,(c,d)) Chris@16: { Chris@16: is >> ch; // get the fourth lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == '(') // read "(a,(", possible: (a,(c)), (a,(c,d)) Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> v; // we extract the third and fourth component Chris@16: Chris@16: c = v.real(); Chris@16: d = v.imag(); Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the ninth lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // format: (a,(c)) or (a,(c,d)) Chris@16: { Chris@16: q = quaternion(a,b,c,d); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // read "(a,b", possible: (a,b), (a,b,c), (a,b,c,d) Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> b; // we extract the second component Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the fifth lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // format: (a,b) Chris@16: { Chris@16: q = quaternion(a,b); Chris@16: } Chris@16: else if (cc == ',') // read "(a,b,", possible: (a,b,c), (a,b,c,d) Chris@16: { Chris@16: is >> c; // we extract the third component Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the seventh lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // format: (a,b,c) Chris@16: { Chris@16: q = quaternion(a,b,c); Chris@16: } Chris@16: else if (cc == ',') // read "(a,b,c,", possible: (a,b,c,d) Chris@16: { Chris@16: is >> d; // we extract the fourth component Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: is >> ch; // get the ninth lexeme Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: cc = ch; Chris@16: #else Chris@16: cc = ct.narrow(ch, char()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: Chris@16: if (cc == ')') // format: (a,b,c,d) Chris@16: { Chris@16: q = quaternion(a,b,c,d); Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: } Chris@16: else // error Chris@16: { Chris@16: is.setstate(::std::ios_base::failbit); Chris@16: } Chris@16: } Chris@16: } Chris@16: else // format: a Chris@16: { Chris@16: is.putback(ch); Chris@16: Chris@16: is >> a; // we extract the first component Chris@16: Chris@16: if (!is.good()) goto finish; Chris@16: Chris@16: q = quaternion(a); Chris@16: } Chris@16: Chris@16: finish: Chris@16: return(is); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: ::std::basic_ostream & operator << ( ::std::basic_ostream & os, Chris@16: quaternion const & q) Chris@16: { Chris@16: ::std::basic_ostringstream s; Chris@101: Chris@16: s.flags(os.flags()); Chris@16: #ifdef BOOST_NO_STD_LOCALE Chris@16: #else Chris@16: s.imbue(os.getloc()); Chris@16: #endif /* BOOST_NO_STD_LOCALE */ Chris@16: s.precision(os.precision()); Chris@16: Chris@16: s << '(' << q.R_component_1() << ',' Chris@16: << q.R_component_2() << ',' Chris@16: << q.R_component_3() << ',' Chris@16: << q.R_component_4() << ')'; Chris@16: Chris@16: return os << s.str(); Chris@16: } Chris@16: Chris@16: Chris@16: // values Chris@16: Chris@16: template Chris@16: inline T real(quaternion const & q) Chris@16: { Chris@16: return(q.real()); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline quaternion unreal(quaternion const & q) Chris@16: { Chris@16: return(q.unreal()); Chris@16: } Chris@16: Chris@16: Chris@16: #define BOOST_QUATERNION_VALARRAY_LOADER \ Chris@16: using ::std::valarray; \ Chris@16: \ Chris@16: valarray temp(4); \ Chris@16: \ Chris@16: temp[0] = q.R_component_1(); \ Chris@16: temp[1] = q.R_component_2(); \ Chris@16: temp[2] = q.R_component_3(); \ Chris@16: temp[3] = q.R_component_4(); Chris@16: Chris@16: Chris@16: template Chris@16: inline T sup(quaternion const & q) Chris@16: { Chris@16: #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP Chris@16: using ::std::abs; Chris@16: #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ Chris@16: Chris@16: BOOST_QUATERNION_VALARRAY_LOADER Chris@16: Chris@16: return((abs(temp).max)()); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline T l1(quaternion const & q) Chris@16: { Chris@16: #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP Chris@16: using ::std::abs; Chris@16: #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ Chris@16: Chris@16: BOOST_QUATERNION_VALARRAY_LOADER Chris@16: Chris@16: return(abs(temp).sum()); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline T abs(quaternion const & q) Chris@16: { Chris@16: #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP Chris@16: using ::std::abs; Chris@16: #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ Chris@16: Chris@16: using ::std::sqrt; Chris@16: Chris@16: BOOST_QUATERNION_VALARRAY_LOADER Chris@16: Chris@16: T maxim = (abs(temp).max)(); // overflow protection Chris@16: Chris@16: if (maxim == static_cast(0)) Chris@16: { Chris@16: return(maxim); Chris@16: } Chris@16: else Chris@16: { Chris@16: T mixam = static_cast(1)/maxim; // prefer multiplications over divisions Chris@16: Chris@16: temp *= mixam; Chris@16: Chris@16: temp *= temp; Chris@16: Chris@16: return(maxim*sqrt(temp.sum())); Chris@16: } Chris@16: Chris@16: //return(sqrt(norm(q))); Chris@16: } Chris@16: Chris@16: Chris@16: #undef BOOST_QUATERNION_VALARRAY_LOADER Chris@16: Chris@16: Chris@16: // Note: This is the Cayley norm, not the Euclidian norm... Chris@16: Chris@16: template Chris@16: inline T norm(quaternionconst & q) Chris@16: { Chris@16: return(real(q*conj(q))); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline quaternion conj(quaternion const & q) Chris@16: { Chris@16: return(quaternion( +q.R_component_1(), Chris@16: -q.R_component_2(), Chris@16: -q.R_component_3(), Chris@16: -q.R_component_4())); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline quaternion spherical( T const & rho, Chris@16: T const & theta, Chris@16: T const & phi1, Chris@16: T const & phi2) Chris@16: { Chris@16: using ::std::cos; Chris@16: using ::std::sin; Chris@16: Chris@16: //T a = cos(theta)*cos(phi1)*cos(phi2); Chris@16: //T b = sin(theta)*cos(phi1)*cos(phi2); Chris@16: //T c = sin(phi1)*cos(phi2); Chris@16: //T d = sin(phi2); Chris@16: Chris@16: T courrant = static_cast(1); Chris@16: Chris@16: T d = sin(phi2); Chris@16: Chris@16: courrant *= cos(phi2); Chris@16: Chris@16: T c = sin(phi1)*courrant; Chris@16: Chris@16: courrant *= cos(phi1); Chris@16: Chris@16: T b = sin(theta)*courrant; Chris@16: T a = cos(theta)*courrant; Chris@16: Chris@16: return(rho*quaternion(a,b,c,d)); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline quaternion semipolar( T const & rho, Chris@16: T const & alpha, Chris@16: T const & theta1, Chris@16: T const & theta2) Chris@16: { Chris@16: using ::std::cos; Chris@16: using ::std::sin; Chris@16: Chris@16: T a = cos(alpha)*cos(theta1); Chris@16: T b = cos(alpha)*sin(theta1); Chris@16: T c = sin(alpha)*cos(theta2); Chris@16: T d = sin(alpha)*sin(theta2); Chris@16: Chris@16: return(rho*quaternion(a,b,c,d)); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline quaternion multipolar( T const & rho1, Chris@16: T const & theta1, Chris@16: T const & rho2, Chris@16: T const & theta2) Chris@16: { Chris@16: using ::std::cos; Chris@16: using ::std::sin; Chris@16: Chris@16: T a = rho1*cos(theta1); Chris@16: T b = rho1*sin(theta1); Chris@16: T c = rho2*cos(theta2); Chris@16: T d = rho2*sin(theta2); Chris@16: Chris@16: return(quaternion(a,b,c,d)); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline quaternion cylindrospherical( T const & t, Chris@16: T const & radius, Chris@16: T const & longitude, Chris@16: T const & latitude) Chris@16: { Chris@16: using ::std::cos; Chris@16: using ::std::sin; Chris@16: Chris@16: Chris@16: Chris@16: T b = radius*cos(longitude)*cos(latitude); Chris@16: T c = radius*sin(longitude)*cos(latitude); Chris@16: T d = radius*sin(latitude); Chris@16: Chris@16: return(quaternion(t,b,c,d)); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline quaternion cylindrical(T const & r, Chris@16: T const & angle, Chris@16: T const & h1, Chris@16: T const & h2) Chris@16: { Chris@16: using ::std::cos; Chris@16: using ::std::sin; Chris@16: Chris@16: T a = r*cos(angle); Chris@16: T b = r*sin(angle); Chris@16: Chris@16: return(quaternion(a,b,h1,h2)); Chris@16: } Chris@16: Chris@16: Chris@16: // transcendentals Chris@16: // (please see the documentation) Chris@16: Chris@16: Chris@16: template Chris@16: inline quaternion exp(quaternion const & q) Chris@16: { Chris@16: using ::std::exp; Chris@16: using ::std::cos; Chris@16: Chris@16: using ::boost::math::sinc_pi; Chris@16: Chris@16: T u = exp(real(q)); Chris@16: Chris@16: T z = abs(unreal(q)); Chris@16: Chris@16: T w = sinc_pi(z); Chris@16: Chris@16: return(u*quaternion(cos(z), Chris@16: w*q.R_component_2(), w*q.R_component_3(), Chris@16: w*q.R_component_4())); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline quaternion cos(quaternion const & q) Chris@16: { Chris@16: using ::std::sin; Chris@16: using ::std::cos; Chris@16: using ::std::cosh; Chris@16: Chris@16: using ::boost::math::sinhc_pi; Chris@16: Chris@16: T z = abs(unreal(q)); Chris@16: Chris@16: T w = -sin(q.real())*sinhc_pi(z); Chris@16: Chris@16: return(quaternion(cos(q.real())*cosh(z), Chris@16: w*q.R_component_2(), w*q.R_component_3(), Chris@16: w*q.R_component_4())); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline quaternion sin(quaternion const & q) Chris@16: { Chris@16: using ::std::sin; Chris@16: using ::std::cos; Chris@16: using ::std::cosh; Chris@16: Chris@16: using ::boost::math::sinhc_pi; Chris@16: Chris@16: T z = abs(unreal(q)); Chris@16: Chris@16: T w = +cos(q.real())*sinhc_pi(z); Chris@16: Chris@16: return(quaternion(sin(q.real())*cosh(z), Chris@16: w*q.R_component_2(), w*q.R_component_3(), Chris@16: w*q.R_component_4())); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline quaternion tan(quaternion const & q) Chris@16: { Chris@16: return(sin(q)/cos(q)); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline quaternion cosh(quaternion const & q) Chris@16: { Chris@16: return((exp(+q)+exp(-q))/static_cast(2)); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline quaternion sinh(quaternion const & q) Chris@16: { Chris@16: return((exp(+q)-exp(-q))/static_cast(2)); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: inline quaternion tanh(quaternion const & q) Chris@16: { Chris@16: return(sinh(q)/cosh(q)); Chris@16: } Chris@16: Chris@16: Chris@16: template Chris@16: quaternion pow(quaternion const & q, Chris@16: int n) Chris@16: { Chris@16: if (n > 1) Chris@16: { Chris@16: int m = n>>1; Chris@16: Chris@16: quaternion result = pow(q, m); Chris@16: Chris@16: result *= result; Chris@16: Chris@16: if (n != (m<<1)) Chris@16: { Chris@16: result *= q; // n odd Chris@16: } Chris@16: Chris@16: return(result); Chris@16: } Chris@16: else if (n == 1) Chris@16: { Chris@16: return(q); Chris@16: } Chris@16: else if (n == 0) Chris@16: { Chris@16: return(quaternion(static_cast(1))); Chris@16: } Chris@16: else /* n < 0 */ Chris@16: { Chris@16: return(pow(quaternion(static_cast(1))/q,-n)); Chris@16: } Chris@16: } Chris@16: Chris@16: Chris@16: // helper templates for converting copy constructors (definition) Chris@16: Chris@16: namespace detail Chris@16: { Chris@16: Chris@16: template< typename T, Chris@16: typename U Chris@16: > Chris@16: quaternion quaternion_type_converter(quaternion const & rhs) Chris@16: { Chris@16: return(quaternion( static_cast(rhs.R_component_1()), Chris@16: static_cast(rhs.R_component_2()), Chris@16: static_cast(rhs.R_component_3()), Chris@16: static_cast(rhs.R_component_4()))); Chris@16: } Chris@16: } Chris@16: } Chris@16: } Chris@16: Chris@16: #endif /* BOOST_QUATERNION_HPP */