diff -r 000000000000 -r e4d67989cc36 ossrv_pub/boost_apis/boost/math/quaternion.hpp --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ossrv_pub/boost_apis/boost/math/quaternion.hpp Tue Feb 02 02:01:42 2010 +0200 @@ -0,0 +1,1924 @@ +// boost quaternion.hpp header file + +// (C) Copyright Hubert Holin 2001. +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) + +// See http://www.boost.org for updates, documentation, and revision history. + +#ifndef BOOST_QUATERNION_HPP +#define BOOST_QUATERNION_HPP + + +#include +#include // for the "<<" and ">>" operators +#include // for the "<<" operator + +#include // for BOOST_NO_STD_LOCALE +#include +#ifndef BOOST_NO_STD_LOCALE + #include // for the "<<" operator +#endif /* BOOST_NO_STD_LOCALE */ + +#include + + + +#include // for the Sinus cardinal +#include // for the Hyperbolic Sinus cardinal + + +namespace boost +{ + namespace math + { +#if BOOST_WORKAROUND(__GNUC__, < 3) + // gcc 2.95.x uses expression templates for valarray calculations, but + // the result is not conforming. We need BOOST_GET_VALARRAY to get an + // actual valarray result when we need to call a member function + #define BOOST_GET_VALARRAY(T,x) ::std::valarray(x) + // gcc 2.95.x has an "std::ios" class that is similar to + // "std::ios_base", so we just use a #define + #define BOOST_IOS_BASE ::std::ios + // gcc 2.x ignores function scope using declarations, + // put them in the scope of the enclosing namespace instead: + using ::std::valarray; + using ::std::sqrt; + using ::std::cos; + using ::std::sin; + using ::std::exp; + using ::std::cosh; +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + +#define BOOST_QUATERNION_ACCESSOR_GENERATOR(type) \ + type real() const \ + { \ + return(a); \ + } \ + \ + quaternion unreal() const \ + { \ + return(quaternion(static_cast(0),b,c,d)); \ + } \ + \ + type R_component_1() const \ + { \ + return(a); \ + } \ + \ + type R_component_2() const \ + { \ + return(b); \ + } \ + \ + type R_component_3() const \ + { \ + return(c); \ + } \ + \ + type R_component_4() const \ + { \ + return(d); \ + } \ + \ + ::std::complex C_component_1() const \ + { \ + return(::std::complex(a,b)); \ + } \ + \ + ::std::complex C_component_2() const \ + { \ + return(::std::complex(c,d)); \ + } + + +#define BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(type) \ + template \ + quaternion & operator = (quaternion const & a_affecter) \ + { \ + a = static_cast(a_affecter.R_component_1()); \ + b = static_cast(a_affecter.R_component_2()); \ + c = static_cast(a_affecter.R_component_3()); \ + d = static_cast(a_affecter.R_component_4()); \ + \ + return(*this); \ + } \ + \ + quaternion & operator = (quaternion const & a_affecter) \ + { \ + a = a_affecter.a; \ + b = a_affecter.b; \ + c = a_affecter.c; \ + d = a_affecter.d; \ + \ + return(*this); \ + } \ + \ + quaternion & operator = (type const & a_affecter) \ + { \ + a = a_affecter; \ + \ + b = c = d = static_cast(0); \ + \ + return(*this); \ + } \ + \ + quaternion & operator = (::std::complex const & a_affecter) \ + { \ + a = a_affecter.real(); \ + b = a_affecter.imag(); \ + \ + c = d = static_cast(0); \ + \ + return(*this); \ + } + + +#define BOOST_QUATERNION_MEMBER_DATA_GENERATOR(type) \ + type a; \ + type b; \ + type c; \ + type d; + + + template + class quaternion + { + public: + + typedef T value_type; + + + // constructor for H seen as R^4 + // (also default constructor) + + explicit quaternion( T const & requested_a = T(), + T const & requested_b = T(), + T const & requested_c = T(), + T const & requested_d = T()) + : a(requested_a), + b(requested_b), + c(requested_c), + d(requested_d) + { + // nothing to do! + } + + + // constructor for H seen as C^2 + + explicit quaternion( ::std::complex const & z0, + ::std::complex const & z1 = ::std::complex()) + : a(z0.real()), + b(z0.imag()), + c(z1.real()), + d(z1.imag()) + { + // nothing to do! + } + + + // UNtemplated copy constructor + // (this is taken care of by the compiler itself) + + + // templated copy constructor + + template + explicit quaternion(quaternion const & a_recopier) + : a(static_cast(a_recopier.R_component_1())), + b(static_cast(a_recopier.R_component_2())), + c(static_cast(a_recopier.R_component_3())), + d(static_cast(a_recopier.R_component_4())) + { + // nothing to do! + } + + + // destructor + // (this is taken care of by the compiler itself) + + + // accessors + // + // Note: Like complex number, quaternions do have a meaningful notion of "real part", + // but unlike them there is no meaningful notion of "imaginary part". + // Instead there is an "unreal part" which itself is a quaternion, and usually + // nothing simpler (as opposed to the complex number case). + // However, for practicallity, there are accessors for the other components + // (these are necessary for the templated copy constructor, for instance). + + BOOST_QUATERNION_ACCESSOR_GENERATOR(T) + + // assignment operators + + BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(T) + + // other assignment-related operators + // + // NOTE: Quaternion multiplication is *NOT* commutative; + // symbolically, "q *= rhs;" means "q = q * rhs;" + // and "q /= rhs;" means "q = q * inverse_of(rhs);" + + quaternion & operator += (T const & rhs) + { + T at = a + rhs; // exception guard + + a = at; + + return(*this); + } + + + quaternion & operator += (::std::complex const & rhs) + { + T at = a + rhs.real(); // exception guard + T bt = b + rhs.imag(); // exception guard + + a = at; + b = bt; + + return(*this); + } + + + template + quaternion & operator += (quaternion const & rhs) + { + T at = a + static_cast(rhs.R_component_1()); // exception guard + T bt = b + static_cast(rhs.R_component_2()); // exception guard + T ct = c + static_cast(rhs.R_component_3()); // exception guard + T dt = d + static_cast(rhs.R_component_4()); // exception guard + + a = at; + b = bt; + c = ct; + d = dt; + + return(*this); + } + + + + quaternion & operator -= (T const & rhs) + { + T at = a - rhs; // exception guard + + a = at; + + return(*this); + } + + + quaternion & operator -= (::std::complex const & rhs) + { + T at = a - rhs.real(); // exception guard + T bt = b - rhs.imag(); // exception guard + + a = at; + b = bt; + + return(*this); + } + + + template + quaternion & operator -= (quaternion const & rhs) + { + T at = a - static_cast(rhs.R_component_1()); // exception guard + T bt = b - static_cast(rhs.R_component_2()); // exception guard + T ct = c - static_cast(rhs.R_component_3()); // exception guard + T dt = d - static_cast(rhs.R_component_4()); // exception guard + + a = at; + b = bt; + c = ct; + d = dt; + + return(*this); + } + + + quaternion & operator *= (T const & rhs) + { + T at = a * rhs; // exception guard + T bt = b * rhs; // exception guard + T ct = c * rhs; // exception guard + T dt = d * rhs; // exception guard + + a = at; + b = bt; + c = ct; + d = dt; + + return(*this); + } + + + quaternion & operator *= (::std::complex const & rhs) + { + T ar = rhs.real(); + T br = rhs.imag(); + + T at = +a*ar-b*br; + T bt = +a*br+b*ar; + T ct = +c*ar+d*br; + T dt = -c*br+d*ar; + + a = at; + b = bt; + c = ct; + d = dt; + + return(*this); + } + + + template + quaternion & operator *= (quaternion const & rhs) + { + T ar = static_cast(rhs.R_component_1()); + T br = static_cast(rhs.R_component_2()); + T cr = static_cast(rhs.R_component_3()); + T dr = static_cast(rhs.R_component_4()); + + T at = +a*ar-b*br-c*cr-d*dr; + T bt = +a*br+b*ar+c*dr-d*cr; //(a*br+ar*b)+(c*dr-cr*d); + T ct = +a*cr-b*dr+c*ar+d*br; //(a*cr+ar*c)+(d*br-dr*b); + T dt = +a*dr+b*cr-c*br+d*ar; //(a*dr+ar*d)+(b*cr-br*c); + + a = at; + b = bt; + c = ct; + d = dt; + + return(*this); + } + + + + quaternion & operator /= (T const & rhs) + { + T at = a / rhs; // exception guard + T bt = b / rhs; // exception guard + T ct = c / rhs; // exception guard + T dt = d / rhs; // exception guard + + a = at; + b = bt; + c = ct; + d = dt; + + return(*this); + } + + + quaternion & operator /= (::std::complex const & rhs) + { + T ar = rhs.real(); + T br = rhs.imag(); + + T denominator = ar*ar+br*br; + + T at = (+a*ar+b*br)/denominator; //(a*ar+b*br)/denominator; + T bt = (-a*br+b*ar)/denominator; //(ar*b-a*br)/denominator; + T ct = (+c*ar-d*br)/denominator; //(ar*c-d*br)/denominator; + T dt = (+c*br+d*ar)/denominator; //(ar*d+br*c)/denominator; + + a = at; + b = bt; + c = ct; + d = dt; + + return(*this); + } + + + template + quaternion & operator /= (quaternion const & rhs) + { + T ar = static_cast(rhs.R_component_1()); + T br = static_cast(rhs.R_component_2()); + T cr = static_cast(rhs.R_component_3()); + T dr = static_cast(rhs.R_component_4()); + + T denominator = ar*ar+br*br+cr*cr+dr*dr; + + T at = (+a*ar+b*br+c*cr+d*dr)/denominator; //(a*ar+b*br+c*cr+d*dr)/denominator; + T bt = (-a*br+b*ar-c*dr+d*cr)/denominator; //((ar*b-a*br)+(cr*d-c*dr))/denominator; + T ct = (-a*cr+b*dr+c*ar-d*br)/denominator; //((ar*c-a*cr)+(dr*b-d*br))/denominator; + T dt = (-a*dr-b*cr+c*br+d*ar)/denominator; //((ar*d-a*dr)+(br*c-b*cr))/denominator; + + a = at; + b = bt; + c = ct; + d = dt; + + return(*this); + } + + + protected: + + BOOST_QUATERNION_MEMBER_DATA_GENERATOR(T) + + + private: + + }; + + + // declaration of quaternion specialization + + template<> class quaternion; + template<> class quaternion; + template<> class quaternion; + + + // helper templates for converting copy constructors (declaration) + + namespace detail + { + + template< typename T, + typename U + > + quaternion quaternion_type_converter(quaternion const & rhs); + } + + + // implementation of quaternion specialization + + +#define BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(type) \ + explicit quaternion( type const & requested_a = static_cast(0), \ + type const & requested_b = static_cast(0), \ + type const & requested_c = static_cast(0), \ + type const & requested_d = static_cast(0)) \ + : a(requested_a), \ + b(requested_b), \ + c(requested_c), \ + d(requested_d) \ + { \ + } \ + \ + explicit quaternion( ::std::complex const & z0, \ + ::std::complex const & z1 = ::std::complex()) \ + : a(z0.real()), \ + b(z0.imag()), \ + c(z1.real()), \ + d(z1.imag()) \ + { \ + } + + +#define BOOST_QUATERNION_MEMBER_ADD_GENERATOR_1(type) \ + quaternion & operator += (type const & rhs) \ + { \ + a += rhs; \ + \ + return(*this); \ + } + +#define BOOST_QUATERNION_MEMBER_ADD_GENERATOR_2(type) \ + quaternion & operator += (::std::complex const & rhs) \ + { \ + a += rhs.real(); \ + b += rhs.imag(); \ + \ + return(*this); \ + } + +#define BOOST_QUATERNION_MEMBER_ADD_GENERATOR_3(type) \ + template \ + quaternion & operator += (quaternion const & rhs) \ + { \ + a += static_cast(rhs.R_component_1()); \ + b += static_cast(rhs.R_component_2()); \ + c += static_cast(rhs.R_component_3()); \ + d += static_cast(rhs.R_component_4()); \ + \ + return(*this); \ + } + +#define BOOST_QUATERNION_MEMBER_SUB_GENERATOR_1(type) \ + quaternion & operator -= (type const & rhs) \ + { \ + a -= rhs; \ + \ + return(*this); \ + } + +#define BOOST_QUATERNION_MEMBER_SUB_GENERATOR_2(type) \ + quaternion & operator -= (::std::complex const & rhs) \ + { \ + a -= rhs.real(); \ + b -= rhs.imag(); \ + \ + return(*this); \ + } + +#define BOOST_QUATERNION_MEMBER_SUB_GENERATOR_3(type) \ + template \ + quaternion & operator -= (quaternion const & rhs) \ + { \ + a -= static_cast(rhs.R_component_1()); \ + b -= static_cast(rhs.R_component_2()); \ + c -= static_cast(rhs.R_component_3()); \ + d -= static_cast(rhs.R_component_4()); \ + \ + return(*this); \ + } + +#define BOOST_QUATERNION_MEMBER_MUL_GENERATOR_1(type) \ + quaternion & operator *= (type const & rhs) \ + { \ + a *= rhs; \ + b *= rhs; \ + c *= rhs; \ + d *= rhs; \ + \ + return(*this); \ + } + +#define BOOST_QUATERNION_MEMBER_MUL_GENERATOR_2(type) \ + quaternion & operator *= (::std::complex const & rhs) \ + { \ + type ar = rhs.real(); \ + type br = rhs.imag(); \ + \ + type at = +a*ar-b*br; \ + type bt = +a*br+b*ar; \ + type ct = +c*ar+d*br; \ + type dt = -c*br+d*ar; \ + \ + a = at; \ + b = bt; \ + c = ct; \ + d = dt; \ + \ + return(*this); \ + } + +#define BOOST_QUATERNION_MEMBER_MUL_GENERATOR_3(type) \ + template \ + quaternion & operator *= (quaternion const & rhs) \ + { \ + type ar = static_cast(rhs.R_component_1()); \ + type br = static_cast(rhs.R_component_2()); \ + type cr = static_cast(rhs.R_component_3()); \ + type dr = static_cast(rhs.R_component_4()); \ + \ + type at = +a*ar-b*br-c*cr-d*dr; \ + type bt = +a*br+b*ar+c*dr-d*cr; \ + type ct = +a*cr-b*dr+c*ar+d*br; \ + type dt = +a*dr+b*cr-c*br+d*ar; \ + \ + a = at; \ + b = bt; \ + c = ct; \ + d = dt; \ + \ + return(*this); \ + } + +// There is quite a lot of repetition in the code below. This is intentional. +// The last conditional block is the normal form, and the others merely +// consist of workarounds for various compiler deficiencies. Hopefuly, when +// more compilers are conformant and we can retire support for those that are +// not, we will be able to remove the clutter. This is makes the situation +// (painfully) explicit. + +#define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_1(type) \ + quaternion & operator /= (type const & rhs) \ + { \ + a /= rhs; \ + b /= rhs; \ + c /= rhs; \ + d /= rhs; \ + \ + return(*this); \ + } + +#if defined(__GNUC__) && (__GNUC__ < 3) + #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \ + quaternion & operator /= (::std::complex const & rhs) \ + { \ + using ::std::valarray; \ + \ + valarray tr(2); \ + \ + tr[0] = rhs.real(); \ + tr[1] = rhs.imag(); \ + \ + type mixam = (BOOST_GET_VALARRAY(type,static_cast(1)/abs(tr)).max)(); \ + \ + tr *= mixam; \ + \ + valarray tt(4); \ + \ + tt[0] = +a*tr[0]+b*tr[1]; \ + tt[1] = -a*tr[1]+b*tr[0]; \ + tt[2] = +c*tr[0]-d*tr[1]; \ + tt[3] = +c*tr[1]+d*tr[0]; \ + \ + tr *= tr; \ + \ + tt *= (mixam/tr.sum()); \ + \ + a = tt[0]; \ + b = tt[1]; \ + c = tt[2]; \ + d = tt[3]; \ + \ + return(*this); \ + } +#elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) + #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \ + quaternion & operator /= (::std::complex const & rhs) \ + { \ + using ::std::valarray; \ + using ::std::abs; \ + \ + valarray tr(2); \ + \ + tr[0] = rhs.real(); \ + tr[1] = rhs.imag(); \ + \ + type mixam = static_cast(1)/(abs(tr).max)(); \ + \ + tr *= mixam; \ + \ + valarray tt(4); \ + \ + tt[0] = +a*tr[0]+b*tr[1]; \ + tt[1] = -a*tr[1]+b*tr[0]; \ + tt[2] = +c*tr[0]-d*tr[1]; \ + tt[3] = +c*tr[1]+d*tr[0]; \ + \ + tr *= tr; \ + \ + tt *= (mixam/tr.sum()); \ + \ + a = tt[0]; \ + b = tt[1]; \ + c = tt[2]; \ + d = tt[3]; \ + \ + return(*this); \ + } +#else + #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \ + quaternion & operator /= (::std::complex const & rhs) \ + { \ + using ::std::valarray; \ + \ + valarray tr(2); \ + \ + tr[0] = rhs.real(); \ + tr[1] = rhs.imag(); \ + \ + type mixam = static_cast(1)/(abs(tr).max)(); \ + \ + tr *= mixam; \ + \ + valarray tt(4); \ + \ + tt[0] = +a*tr[0]+b*tr[1]; \ + tt[1] = -a*tr[1]+b*tr[0]; \ + tt[2] = +c*tr[0]-d*tr[1]; \ + tt[3] = +c*tr[1]+d*tr[0]; \ + \ + tr *= tr; \ + \ + tt *= (mixam/tr.sum()); \ + \ + a = tt[0]; \ + b = tt[1]; \ + c = tt[2]; \ + d = tt[3]; \ + \ + return(*this); \ + } +#endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ + +#if defined(__GNUC__) && (__GNUC__ < 3) + #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type) \ + template \ + quaternion & operator /= (quaternion const & rhs) \ + { \ + using ::std::valarray; \ + \ + valarray tr(4); \ + \ + tr[0] = static_cast(rhs.R_component_1()); \ + tr[1] = static_cast(rhs.R_component_2()); \ + tr[2] = static_cast(rhs.R_component_3()); \ + tr[3] = static_cast(rhs.R_component_4()); \ + \ + type mixam = (BOOST_GET_VALARRAY(type,static_cast(1)/abs(tr)).max)(); \ + \ + tr *= mixam; \ + \ + valarray tt(4); \ + \ + tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \ + tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \ + tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \ + tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \ + \ + tr *= tr; \ + \ + tt *= (mixam/tr.sum()); \ + \ + a = tt[0]; \ + b = tt[1]; \ + c = tt[2]; \ + d = tt[3]; \ + \ + return(*this); \ + } +#elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) + #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type) \ + template \ + quaternion & operator /= (quaternion const & rhs) \ + { \ + using ::std::valarray; \ + using ::std::abs; \ + \ + valarray tr(4); \ + \ + tr[0] = static_cast(rhs.R_component_1()); \ + tr[1] = static_cast(rhs.R_component_2()); \ + tr[2] = static_cast(rhs.R_component_3()); \ + tr[3] = static_cast(rhs.R_component_4()); \ + \ + type mixam = static_cast(1)/(abs(tr).max)(); \ + \ + tr *= mixam; \ + \ + valarray tt(4); \ + \ + tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \ + tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \ + tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \ + tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \ + \ + tr *= tr; \ + \ + tt *= (mixam/tr.sum()); \ + \ + a = tt[0]; \ + b = tt[1]; \ + c = tt[2]; \ + d = tt[3]; \ + \ + return(*this); \ + } +#else + #define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type) \ + template \ + quaternion & operator /= (quaternion const & rhs) \ + { \ + using ::std::valarray; \ + \ + valarray tr(4); \ + \ + tr[0] = static_cast(rhs.R_component_1()); \ + tr[1] = static_cast(rhs.R_component_2()); \ + tr[2] = static_cast(rhs.R_component_3()); \ + tr[3] = static_cast(rhs.R_component_4()); \ + \ + type mixam = static_cast(1)/(abs(tr).max)(); \ + \ + tr *= mixam; \ + \ + valarray tt(4); \ + \ + tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \ + tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \ + tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \ + tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \ + \ + tr *= tr; \ + \ + tt *= (mixam/tr.sum()); \ + \ + a = tt[0]; \ + b = tt[1]; \ + c = tt[2]; \ + d = tt[3]; \ + \ + return(*this); \ + } +#endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ + +#define BOOST_QUATERNION_MEMBER_ADD_GENERATOR(type) \ + BOOST_QUATERNION_MEMBER_ADD_GENERATOR_1(type) \ + BOOST_QUATERNION_MEMBER_ADD_GENERATOR_2(type) \ + BOOST_QUATERNION_MEMBER_ADD_GENERATOR_3(type) + +#define BOOST_QUATERNION_MEMBER_SUB_GENERATOR(type) \ + BOOST_QUATERNION_MEMBER_SUB_GENERATOR_1(type) \ + BOOST_QUATERNION_MEMBER_SUB_GENERATOR_2(type) \ + BOOST_QUATERNION_MEMBER_SUB_GENERATOR_3(type) + +#define BOOST_QUATERNION_MEMBER_MUL_GENERATOR(type) \ + BOOST_QUATERNION_MEMBER_MUL_GENERATOR_1(type) \ + BOOST_QUATERNION_MEMBER_MUL_GENERATOR_2(type) \ + BOOST_QUATERNION_MEMBER_MUL_GENERATOR_3(type) + +#define BOOST_QUATERNION_MEMBER_DIV_GENERATOR(type) \ + BOOST_QUATERNION_MEMBER_DIV_GENERATOR_1(type) \ + BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \ + BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type) + +#define BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(type) \ + BOOST_QUATERNION_MEMBER_ADD_GENERATOR(type) \ + BOOST_QUATERNION_MEMBER_SUB_GENERATOR(type) \ + BOOST_QUATERNION_MEMBER_MUL_GENERATOR(type) \ + BOOST_QUATERNION_MEMBER_DIV_GENERATOR(type) + + + template<> + class quaternion + { + public: + + typedef float value_type; + + BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(float) + + // UNtemplated copy constructor + // (this is taken care of by the compiler itself) + + // explicit copy constructors (precision-loosing converters) + + explicit quaternion(quaternion const & a_recopier) + { + *this = detail::quaternion_type_converter(a_recopier); + } + + explicit quaternion(quaternion const & a_recopier) + { + *this = detail::quaternion_type_converter(a_recopier); + } + + // destructor + // (this is taken care of by the compiler itself) + + // accessors + // + // Note: Like complex number, quaternions do have a meaningful notion of "real part", + // but unlike them there is no meaningful notion of "imaginary part". + // Instead there is an "unreal part" which itself is a quaternion, and usually + // nothing simpler (as opposed to the complex number case). + // However, for practicallity, there are accessors for the other components + // (these are necessary for the templated copy constructor, for instance). + + BOOST_QUATERNION_ACCESSOR_GENERATOR(float) + + // assignment operators + + BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(float) + + // other assignment-related operators + // + // NOTE: Quaternion multiplication is *NOT* commutative; + // symbolically, "q *= rhs;" means "q = q * rhs;" + // and "q /= rhs;" means "q = q * inverse_of(rhs);" + + BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(float) + + + protected: + + BOOST_QUATERNION_MEMBER_DATA_GENERATOR(float) + + + private: + + }; + + + template<> + class quaternion + { + public: + + typedef double value_type; + + BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(double) + + // UNtemplated copy constructor + // (this is taken care of by the compiler itself) + + // converting copy constructor + + explicit quaternion(quaternion const & a_recopier) + { + *this = detail::quaternion_type_converter(a_recopier); + } + + // explicit copy constructors (precision-loosing converters) + + explicit quaternion(quaternion const & a_recopier) + { + *this = detail::quaternion_type_converter(a_recopier); + } + + // destructor + // (this is taken care of by the compiler itself) + + // accessors + // + // Note: Like complex number, quaternions do have a meaningful notion of "real part", + // but unlike them there is no meaningful notion of "imaginary part". + // Instead there is an "unreal part" which itself is a quaternion, and usually + // nothing simpler (as opposed to the complex number case). + // However, for practicallity, there are accessors for the other components + // (these are necessary for the templated copy constructor, for instance). + + BOOST_QUATERNION_ACCESSOR_GENERATOR(double) + + // assignment operators + + BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(double) + + // other assignment-related operators + // + // NOTE: Quaternion multiplication is *NOT* commutative; + // symbolically, "q *= rhs;" means "q = q * rhs;" + // and "q /= rhs;" means "q = q * inverse_of(rhs);" + + BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(double) + + + protected: + + BOOST_QUATERNION_MEMBER_DATA_GENERATOR(double) + + + private: + + }; + + + template<> + class quaternion + { + public: + + typedef long double value_type; + + BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(long double) + + // UNtemplated copy constructor + // (this is taken care of by the compiler itself) + + // converting copy constructors + + explicit quaternion(quaternion const & a_recopier) + { + *this = detail::quaternion_type_converter(a_recopier); + } + + explicit quaternion(quaternion const & a_recopier) + { + *this = detail::quaternion_type_converter(a_recopier); + } + + // destructor + // (this is taken care of by the compiler itself) + + // accessors + // + // Note: Like complex number, quaternions do have a meaningful notion of "real part", + // but unlike them there is no meaningful notion of "imaginary part". + // Instead there is an "unreal part" which itself is a quaternion, and usually + // nothing simpler (as opposed to the complex number case). + // However, for practicallity, there are accessors for the other components + // (these are necessary for the templated copy constructor, for instance). + + BOOST_QUATERNION_ACCESSOR_GENERATOR(long double) + + // assignment operators + + BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(long double) + + // other assignment-related operators + // + // NOTE: Quaternion multiplication is *NOT* commutative; + // symbolically, "q *= rhs;" means "q = q * rhs;" + // and "q /= rhs;" means "q = q * inverse_of(rhs);" + + BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(long double) + + + protected: + + BOOST_QUATERNION_MEMBER_DATA_GENERATOR(long double) + + + private: + + }; + + +#undef BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR +#undef BOOST_QUATERNION_MEMBER_ADD_GENERATOR +#undef BOOST_QUATERNION_MEMBER_SUB_GENERATOR +#undef BOOST_QUATERNION_MEMBER_MUL_GENERATOR +#undef BOOST_QUATERNION_MEMBER_DIV_GENERATOR +#undef BOOST_QUATERNION_MEMBER_ADD_GENERATOR_1 +#undef BOOST_QUATERNION_MEMBER_ADD_GENERATOR_2 +#undef BOOST_QUATERNION_MEMBER_ADD_GENERATOR_3 +#undef BOOST_QUATERNION_MEMBER_SUB_GENERATOR_1 +#undef BOOST_QUATERNION_MEMBER_SUB_GENERATOR_2 +#undef BOOST_QUATERNION_MEMBER_SUB_GENERATOR_3 +#undef BOOST_QUATERNION_MEMBER_MUL_GENERATOR_1 +#undef BOOST_QUATERNION_MEMBER_MUL_GENERATOR_2 +#undef BOOST_QUATERNION_MEMBER_MUL_GENERATOR_3 +#undef BOOST_QUATERNION_MEMBER_DIV_GENERATOR_1 +#undef BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2 +#undef BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3 + +#undef BOOST_QUATERNION_CONSTRUCTOR_GENERATOR + + +#undef BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR + +#undef BOOST_QUATERNION_MEMBER_DATA_GENERATOR + +#undef BOOST_QUATERNION_ACCESSOR_GENERATOR + + + // operators + +#define BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) \ + { \ + quaternion res(lhs); \ + res op##= rhs; \ + return(res); \ + } + +#define BOOST_QUATERNION_OPERATOR_GENERATOR_1_L(op) \ + template \ + inline quaternion operator op (T const & lhs, quaternion const & rhs) \ + BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) + +#define BOOST_QUATERNION_OPERATOR_GENERATOR_1_R(op) \ + template \ + inline quaternion operator op (quaternion const & lhs, T const & rhs) \ + BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) + +#define BOOST_QUATERNION_OPERATOR_GENERATOR_2_L(op) \ + template \ + inline quaternion operator op (::std::complex const & lhs, quaternion const & rhs) \ + BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) + +#define BOOST_QUATERNION_OPERATOR_GENERATOR_2_R(op) \ + template \ + inline quaternion operator op (quaternion const & lhs, ::std::complex const & rhs) \ + BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) + +#define BOOST_QUATERNION_OPERATOR_GENERATOR_3(op) \ + template \ + inline quaternion operator op (quaternion const & lhs, quaternion const & rhs) \ + BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) + +#define BOOST_QUATERNION_OPERATOR_GENERATOR(op) \ + BOOST_QUATERNION_OPERATOR_GENERATOR_1_L(op) \ + BOOST_QUATERNION_OPERATOR_GENERATOR_1_R(op) \ + BOOST_QUATERNION_OPERATOR_GENERATOR_2_L(op) \ + BOOST_QUATERNION_OPERATOR_GENERATOR_2_R(op) \ + BOOST_QUATERNION_OPERATOR_GENERATOR_3(op) + + + BOOST_QUATERNION_OPERATOR_GENERATOR(+) + BOOST_QUATERNION_OPERATOR_GENERATOR(-) + BOOST_QUATERNION_OPERATOR_GENERATOR(*) + BOOST_QUATERNION_OPERATOR_GENERATOR(/) + + +#undef BOOST_QUATERNION_OPERATOR_GENERATOR + +#undef BOOST_QUATERNION_OPERATOR_GENERATOR_1_L +#undef BOOST_QUATERNION_OPERATOR_GENERATOR_1_R +#undef BOOST_QUATERNION_OPERATOR_GENERATOR_2_L +#undef BOOST_QUATERNION_OPERATOR_GENERATOR_2_R +#undef BOOST_QUATERNION_OPERATOR_GENERATOR_3 + +#undef BOOST_QUATERNION_OPERATOR_GENERATOR_BODY + + + template + inline quaternion operator + (quaternion const & q) + { + return(q); + } + + + template + inline quaternion operator - (quaternion const & q) + { + return(quaternion(-q.R_component_1(),-q.R_component_2(),-q.R_component_3(),-q.R_component_4())); + } + + + template + inline bool operator == (T const & lhs, quaternion const & rhs) + { + return ( + (rhs.R_component_1() == lhs)&& + (rhs.R_component_2() == static_cast(0))&& + (rhs.R_component_3() == static_cast(0))&& + (rhs.R_component_4() == static_cast(0)) + ); + } + + + template + inline bool operator == (quaternion const & lhs, T const & rhs) + { + return ( + (lhs.R_component_1() == rhs)&& + (lhs.R_component_2() == static_cast(0))&& + (lhs.R_component_3() == static_cast(0))&& + (lhs.R_component_4() == static_cast(0)) + ); + } + + + template + inline bool operator == (::std::complex const & lhs, quaternion const & rhs) + { + return ( + (rhs.R_component_1() == lhs.real())&& + (rhs.R_component_2() == lhs.imag())&& + (rhs.R_component_3() == static_cast(0))&& + (rhs.R_component_4() == static_cast(0)) + ); + } + + + template + inline bool operator == (quaternion const & lhs, ::std::complex const & rhs) + { + return ( + (lhs.R_component_1() == rhs.real())&& + (lhs.R_component_2() == rhs.imag())&& + (lhs.R_component_3() == static_cast(0))&& + (lhs.R_component_4() == static_cast(0)) + ); + } + + + template + inline bool operator == (quaternion const & lhs, quaternion const & rhs) + { + return ( + (rhs.R_component_1() == lhs.R_component_1())&& + (rhs.R_component_2() == lhs.R_component_2())&& + (rhs.R_component_3() == lhs.R_component_3())&& + (rhs.R_component_4() == lhs.R_component_4()) + ); + } + + +#define BOOST_QUATERNION_NOT_EQUAL_GENERATOR \ + { \ + return(!(lhs == rhs)); \ + } + + template + inline bool operator != (T const & lhs, quaternion const & rhs) + BOOST_QUATERNION_NOT_EQUAL_GENERATOR + + template + inline bool operator != (quaternion const & lhs, T const & rhs) + BOOST_QUATERNION_NOT_EQUAL_GENERATOR + + template + inline bool operator != (::std::complex const & lhs, quaternion const & rhs) + BOOST_QUATERNION_NOT_EQUAL_GENERATOR + + template + inline bool operator != (quaternion const & lhs, ::std::complex const & rhs) + BOOST_QUATERNION_NOT_EQUAL_GENERATOR + + template + inline bool operator != (quaternion const & lhs, quaternion const & rhs) + BOOST_QUATERNION_NOT_EQUAL_GENERATOR + +#undef BOOST_QUATERNION_NOT_EQUAL_GENERATOR + + + // Note: we allow the following formats, whith a, b, c, and d reals + // a + // (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)) +#if BOOST_WORKAROUND(__GNUC__, < 3) + template + std::istream & operator >> ( ::std::istream & is, + quaternion & q) +#else + template + ::std::basic_istream & operator >> ( ::std::basic_istream & is, + quaternion & q) +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + { +#if BOOST_WORKAROUND(__GNUC__, < 3) + typedef char charT; +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + +#ifdef BOOST_NO_STD_LOCALE +#else + const ::std::ctype & ct = ::std::use_facet< ::std::ctype >(is.getloc()); +#endif /* BOOST_NO_STD_LOCALE */ + + T a = T(); + T b = T(); + T c = T(); + T d = T(); + + ::std::complex u = ::std::complex(); + ::std::complex v = ::std::complex(); + + charT ch = charT(); + char cc; + + is >> ch; // get the first lexeme + + if (!is.good()) goto finish; + +#ifdef BOOST_NO_STD_LOCALE + cc = ch; +#else + cc = ct.narrow(ch, char()); +#endif /* BOOST_NO_STD_LOCALE */ + + 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,)) + { + is >> ch; // get the second lexeme + + if (!is.good()) goto finish; + +#ifdef BOOST_NO_STD_LOCALE + cc = ch; +#else + cc = ct.narrow(ch, char()); +#endif /* BOOST_NO_STD_LOCALE */ + + if (cc == '(') // read "((", possible: ((a)), ((a),c), ((a),(c)), ((a),(c,d)), ((a,b)), ((a,b),c), ((a,b),(c)), ((a,b,),(c,d,)) + { + is.putback(ch); + + is >> u; // we extract the first and second components + a = u.real(); + b = u.imag(); + + if (!is.good()) goto finish; + + is >> ch; // get the next lexeme + + if (!is.good()) goto finish; + +#ifdef BOOST_NO_STD_LOCALE + cc = ch; +#else + cc = ct.narrow(ch, char()); +#endif /* BOOST_NO_STD_LOCALE */ + + if (cc == ')') // format: ((a)) or ((a,b)) + { + q = quaternion(a,b); + } + 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,)) + { + is >> v; // we extract the third and fourth components + c = v.real(); + d = v.imag(); + + if (!is.good()) goto finish; + + is >> ch; // get the last lexeme + + if (!is.good()) goto finish; + +#ifdef BOOST_NO_STD_LOCALE + cc = ch; +#else + cc = ct.narrow(ch, char()); +#endif /* BOOST_NO_STD_LOCALE */ + + if (cc == ')') // format: ((a),c), ((a),(c)), ((a),(c,d)), ((a,b),c), ((a,b),(c)) or ((a,b,),(c,d,)) + { + q = quaternion(a,b,c,d); + } + else // error + { +#if BOOST_WORKAROUND(__GNUC__, < 3) + is.setstate(::std::ios::failbit); +#else + is.setstate(::std::ios_base::failbit); +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + } + } + else // error + { +#if BOOST_WORKAROUND(__GNUC__, < 3) + is.setstate(::std::ios::failbit); +#else + is.setstate(::std::ios_base::failbit); +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + } + } + else // read "(a", possible: (a), (a,b), (a,b,c), (a,b,c,d), (a,(c)), (a,(c,d)) + { + is.putback(ch); + + is >> a; // we extract the first component + + if (!is.good()) goto finish; + + is >> ch; // get the third lexeme + + if (!is.good()) goto finish; + +#ifdef BOOST_NO_STD_LOCALE + cc = ch; +#else + cc = ct.narrow(ch, char()); +#endif /* BOOST_NO_STD_LOCALE */ + + if (cc == ')') // format: (a) + { + q = quaternion(a); + } + else if (cc == ',') // read "(a,", possible: (a,b), (a,b,c), (a,b,c,d), (a,(c)), (a,(c,d)) + { + is >> ch; // get the fourth lexeme + + if (!is.good()) goto finish; + +#ifdef BOOST_NO_STD_LOCALE + cc = ch; +#else + cc = ct.narrow(ch, char()); +#endif /* BOOST_NO_STD_LOCALE */ + + if (cc == '(') // read "(a,(", possible: (a,(c)), (a,(c,d)) + { + is.putback(ch); + + is >> v; // we extract the third and fourth component + + c = v.real(); + d = v.imag(); + + if (!is.good()) goto finish; + + is >> ch; // get the ninth lexeme + + if (!is.good()) goto finish; + +#ifdef BOOST_NO_STD_LOCALE + cc = ch; +#else + cc = ct.narrow(ch, char()); +#endif /* BOOST_NO_STD_LOCALE */ + + if (cc == ')') // format: (a,(c)) or (a,(c,d)) + { + q = quaternion(a,b,c,d); + } + else // error + { +#if BOOST_WORKAROUND(__GNUC__, < 3) + is.setstate(::std::ios::failbit); +#else + is.setstate(::std::ios_base::failbit); +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + } + } + else // read "(a,b", possible: (a,b), (a,b,c), (a,b,c,d) + { + is.putback(ch); + + is >> b; // we extract the second component + + if (!is.good()) goto finish; + + is >> ch; // get the fifth lexeme + + if (!is.good()) goto finish; + +#ifdef BOOST_NO_STD_LOCALE + cc = ch; +#else + cc = ct.narrow(ch, char()); +#endif /* BOOST_NO_STD_LOCALE */ + + if (cc == ')') // format: (a,b) + { + q = quaternion(a,b); + } + else if (cc == ',') // read "(a,b,", possible: (a,b,c), (a,b,c,d) + { + is >> c; // we extract the third component + + if (!is.good()) goto finish; + + is >> ch; // get the seventh lexeme + + if (!is.good()) goto finish; + +#ifdef BOOST_NO_STD_LOCALE + cc = ch; +#else + cc = ct.narrow(ch, char()); +#endif /* BOOST_NO_STD_LOCALE */ + + if (cc == ')') // format: (a,b,c) + { + q = quaternion(a,b,c); + } + else if (cc == ',') // read "(a,b,c,", possible: (a,b,c,d) + { + is >> d; // we extract the fourth component + + if (!is.good()) goto finish; + + is >> ch; // get the ninth lexeme + + if (!is.good()) goto finish; + +#ifdef BOOST_NO_STD_LOCALE + cc = ch; +#else + cc = ct.narrow(ch, char()); +#endif /* BOOST_NO_STD_LOCALE */ + + if (cc == ')') // format: (a,b,c,d) + { + q = quaternion(a,b,c,d); + } + else // error + { +#if BOOST_WORKAROUND(__GNUC__, < 3) + is.setstate(::std::ios::failbit); +#else + is.setstate(::std::ios_base::failbit); +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + } + } + else // error + { +#if BOOST_WORKAROUND(__GNUC__, < 3) + is.setstate(::std::ios::failbit); +#else + is.setstate(::std::ios_base::failbit); +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + } + } + else // error + { +#if BOOST_WORKAROUND(__GNUC__, < 3) + is.setstate(::std::ios::failbit); +#else + is.setstate(::std::ios_base::failbit); +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + } + } + } + else // error + { +#if BOOST_WORKAROUND(__GNUC__, < 3) + is.setstate(::std::ios::failbit); +#else + is.setstate(::std::ios_base::failbit); +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + } + } + } + else // format: a + { + is.putback(ch); + + is >> a; // we extract the first component + + if (!is.good()) goto finish; + + q = quaternion(a); + } + + finish: + return(is); + } + + +#if BOOST_WORKAROUND(__GNUC__, < 3) + template + ::std::ostream & operator << ( ::std::ostream & os, + quaternion const & q) +#else + template + ::std::basic_ostream & operator << ( ::std::basic_ostream & os, + quaternion const & q) +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + { +#if BOOST_WORKAROUND(__GNUC__, < 3) + ::std::ostringstream s; +#else + ::std::basic_ostringstream s; +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + + s.flags(os.flags()); +#ifdef BOOST_NO_STD_LOCALE +#else + s.imbue(os.getloc()); +#endif /* BOOST_NO_STD_LOCALE */ + s.precision(os.precision()); + + s << '(' << q.R_component_1() << ',' + << q.R_component_2() << ',' + << q.R_component_3() << ',' + << q.R_component_4() << ')'; + + return os << s.str(); + } + + + // values + + template + inline T real(quaternion const & q) + { + return(q.real()); + } + + + template + inline quaternion unreal(quaternion const & q) + { + return(q.unreal()); + } + + +#define BOOST_QUATERNION_VALARRAY_LOADER \ + using ::std::valarray; \ + \ + valarray temp(4); \ + \ + temp[0] = q.R_component_1(); \ + temp[1] = q.R_component_2(); \ + temp[2] = q.R_component_3(); \ + temp[3] = q.R_component_4(); + + + template + inline T sup(quaternion const & q) + { +#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP + using ::std::abs; +#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ + + BOOST_QUATERNION_VALARRAY_LOADER + +#if BOOST_WORKAROUND(__GNUC__, < 3) + return((BOOST_GET_VALARRAY(T, abs(temp)).max)()); +#else + return((abs(temp).max)()); +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + } + + + template + inline T l1(quaternion const & q) + { +#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP + using ::std::abs; +#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ + + BOOST_QUATERNION_VALARRAY_LOADER + +#if BOOST_WORKAROUND(__GNUC__, < 3) + return(BOOST_GET_VALARRAY(T, abs(temp)).sum()); +#else + return(abs(temp).sum()); +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + } + + + template + inline T abs(quaternion const & q) + { +#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP + using ::std::abs; +#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ + + using ::std::sqrt; + + BOOST_QUATERNION_VALARRAY_LOADER + +#if BOOST_WORKAROUND(__GNUC__, < 3) + T maxim = (BOOST_GET_VALARRAY(T, abs(temp)).max)(); // overflow protection +#else + T maxim = (abs(temp).max)(); // overflow protection +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + + if (maxim == static_cast(0)) + { + return(maxim); + } + else + { + T mixam = static_cast(1)/maxim; // prefer multiplications over divisions + + temp *= mixam; + + temp *= temp; + + return(maxim*sqrt(temp.sum())); + } + + //return(sqrt(norm(q))); + } + + +#undef BOOST_QUATERNION_VALARRAY_LOADER + + + // Note: This is the Cayley norm, not the Euclidian norm... + + template + inline T norm(quaternionconst & q) + { + return(real(q*conj(q))); + } + + + template + inline quaternion conj(quaternion const & q) + { + return(quaternion( +q.R_component_1(), + -q.R_component_2(), + -q.R_component_3(), + -q.R_component_4())); + } + + + template + inline quaternion spherical( T const & rho, + T const & theta, + T const & phi1, + T const & phi2) + { + using ::std::cos; + using ::std::sin; + + //T a = cos(theta)*cos(phi1)*cos(phi2); + //T b = sin(theta)*cos(phi1)*cos(phi2); + //T c = sin(phi1)*cos(phi2); + //T d = sin(phi2); + + T courrant = static_cast(1); + + T d = sin(phi2); + + courrant *= cos(phi2); + + T c = sin(phi1)*courrant; + + courrant *= cos(phi1); + + T b = sin(theta)*courrant; + T a = cos(theta)*courrant; + + return(rho*quaternion(a,b,c,d)); + } + + + template + inline quaternion semipolar( T const & rho, + T const & alpha, + T const & theta1, + T const & theta2) + { + using ::std::cos; + using ::std::sin; + + T a = cos(alpha)*cos(theta1); + T b = cos(alpha)*sin(theta1); + T c = sin(alpha)*cos(theta2); + T d = sin(alpha)*sin(theta2); + + return(rho*quaternion(a,b,c,d)); + } + + + template + inline quaternion multipolar( T const & rho1, + T const & theta1, + T const & rho2, + T const & theta2) + { + using ::std::cos; + using ::std::sin; + + T a = rho1*cos(theta1); + T b = rho1*sin(theta1); + T c = rho2*cos(theta2); + T d = rho2*sin(theta2); + + return(quaternion(a,b,c,d)); + } + + + template + inline quaternion cylindrospherical( T const & t, + T const & radius, + T const & longitude, + T const & latitude) + { + using ::std::cos; + using ::std::sin; + + + + T b = radius*cos(longitude)*cos(latitude); + T c = radius*sin(longitude)*cos(latitude); + T d = radius*sin(latitude); + + return(quaternion(t,b,c,d)); + } + + + template + inline quaternion cylindrical(T const & r, + T const & angle, + T const & h1, + T const & h2) + { + using ::std::cos; + using ::std::sin; + + T a = r*cos(angle); + T b = r*sin(angle); + + return(quaternion(a,b,h1,h2)); + } + + + // transcendentals + // (please see the documentation) + + + template + inline quaternion exp(quaternion const & q) + { + using ::std::exp; + using ::std::cos; + + using ::boost::math::sinc_pi; + + T u = exp(real(q)); + + T z = abs(unreal(q)); + + T w = sinc_pi(z); + + return(u*quaternion(cos(z), + w*q.R_component_2(), w*q.R_component_3(), + w*q.R_component_4())); + } + + + template + inline quaternion cos(quaternion const & q) + { + using ::std::sin; + using ::std::cos; + using ::std::cosh; + + using ::boost::math::sinhc_pi; + + T z = abs(unreal(q)); + + T w = -sin(q.real())*sinhc_pi(z); + + return(quaternion(cos(q.real())*cosh(z), + w*q.R_component_2(), w*q.R_component_3(), + w*q.R_component_4())); + } + + + template + inline quaternion sin(quaternion const & q) + { + using ::std::sin; + using ::std::cos; + using ::std::cosh; + + using ::boost::math::sinhc_pi; + + T z = abs(unreal(q)); + + T w = +cos(q.real())*sinhc_pi(z); + + return(quaternion(sin(q.real())*cosh(z), + w*q.R_component_2(), w*q.R_component_3(), + w*q.R_component_4())); + } + + + template + inline quaternion tan(quaternion const & q) + { + return(sin(q)/cos(q)); + } + + + template + inline quaternion cosh(quaternion const & q) + { + return((exp(+q)+exp(-q))/static_cast(2)); + } + + + template + inline quaternion sinh(quaternion const & q) + { + return((exp(+q)-exp(-q))/static_cast(2)); + } + + + template + inline quaternion tanh(quaternion const & q) + { + return(sinh(q)/cosh(q)); + } + + + template + quaternion pow(quaternion const & q, + int n) + { + if (n > 1) + { + int m = n>>1; + + quaternion result = pow(q, m); + + result *= result; + + if (n != (m<<1)) + { + result *= q; // n odd + } + + return(result); + } + else if (n == 1) + { + return(q); + } + else if (n == 0) + { + return(quaternion(1)); + } + else /* n < 0 */ + { + return(pow(quaternion(1)/q,-n)); + } + } + + + // helper templates for converting copy constructors (definition) + + namespace detail + { + + template< typename T, + typename U + > + quaternion quaternion_type_converter(quaternion const & rhs) + { + return(quaternion( static_cast(rhs.R_component_1()), + static_cast(rhs.R_component_2()), + static_cast(rhs.R_component_3()), + static_cast(rhs.R_component_4()))); + } + } + } +} + + +#if BOOST_WORKAROUND(__GNUC__, < 3) + #undef BOOST_GET_VALARRAY +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ + + +#endif /* BOOST_QUATERNION_HPP */