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// boost quaternion.hpp header file
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// (C) Copyright Hubert Holin 2001.
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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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// See http://www.boost.org for updates, documentation, and revision history.
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#ifndef BOOST_QUATERNION_HPP
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#define BOOST_QUATERNION_HPP
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#include <complex>
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#include <iosfwd> // for the "<<" and ">>" operators
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#include <sstream> // for the "<<" operator
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#include <boost/config.hpp> // for BOOST_NO_STD_LOCALE
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#include <boost/detail/workaround.hpp>
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#ifndef BOOST_NO_STD_LOCALE
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#include <locale> // for the "<<" operator
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#endif /* BOOST_NO_STD_LOCALE */
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#include <valarray>
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#include <boost/math/special_functions/sinc.hpp> // for the Sinus cardinal
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#include <boost/math/special_functions/sinhc.hpp> // for the Hyperbolic Sinus cardinal
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namespace boost
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{
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namespace math
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{
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#if BOOST_WORKAROUND(__GNUC__, < 3)
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// gcc 2.95.x uses expression templates for valarray calculations, but
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// the result is not conforming. We need BOOST_GET_VALARRAY to get an
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// actual valarray result when we need to call a member function
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#define BOOST_GET_VALARRAY(T,x) ::std::valarray<T>(x)
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// gcc 2.95.x has an "std::ios" class that is similar to
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// "std::ios_base", so we just use a #define
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#define BOOST_IOS_BASE ::std::ios
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// gcc 2.x ignores function scope using declarations,
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// put them in the scope of the enclosing namespace instead:
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using ::std::valarray;
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using ::std::sqrt;
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using ::std::cos;
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using ::std::sin;
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using ::std::exp;
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using ::std::cosh;
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#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
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#define BOOST_QUATERNION_ACCESSOR_GENERATOR(type) \
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type real() const \
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{ \
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return(a); \
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} \
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\
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quaternion<type> unreal() const \
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{ \
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return(quaternion<type>(static_cast<type>(0),b,c,d)); \
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} \
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\
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type R_component_1() const \
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{ \
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return(a); \
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} \
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\
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type R_component_2() const \
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{ \
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return(b); \
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} \
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\
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type R_component_3() const \
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{ \
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return(c); \
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} \
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\
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type R_component_4() const \
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{ \
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return(d); \
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} \
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\
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::std::complex<type> C_component_1() const \
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{ \
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return(::std::complex<type>(a,b)); \
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} \
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\
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::std::complex<type> C_component_2() const \
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{ \
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return(::std::complex<type>(c,d)); \
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}
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#define BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(type) \
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template<typename X> \
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quaternion<type> & operator = (quaternion<X> const & a_affecter) \
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{ \
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a = static_cast<type>(a_affecter.R_component_1()); \
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b = static_cast<type>(a_affecter.R_component_2()); \
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c = static_cast<type>(a_affecter.R_component_3()); \
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d = static_cast<type>(a_affecter.R_component_4()); \
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\
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return(*this); \
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} \
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\
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quaternion<type> & operator = (quaternion<type> const & a_affecter) \
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{ \
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a = a_affecter.a; \
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b = a_affecter.b; \
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c = a_affecter.c; \
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d = a_affecter.d; \
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\
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return(*this); \
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} \
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\
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quaternion<type> & operator = (type const & a_affecter) \
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{ \
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a = a_affecter; \
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\
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b = c = d = static_cast<type>(0); \
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\
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return(*this); \
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} \
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\
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quaternion<type> & operator = (::std::complex<type> const & a_affecter) \
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{ \
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a = a_affecter.real(); \
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b = a_affecter.imag(); \
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\
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c = d = static_cast<type>(0); \
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\
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return(*this); \
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}
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#define BOOST_QUATERNION_MEMBER_DATA_GENERATOR(type) \
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type a; \
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type b; \
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type c; \
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type d;
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template<typename T>
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class quaternion
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{
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public:
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typedef T value_type;
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// constructor for H seen as R^4
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// (also default constructor)
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explicit quaternion( T const & requested_a = T(),
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T const & requested_b = T(),
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T const & requested_c = T(),
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T const & requested_d = T())
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: a(requested_a),
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b(requested_b),
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c(requested_c),
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d(requested_d)
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{
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// nothing to do!
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}
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// constructor for H seen as C^2
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explicit quaternion( ::std::complex<T> const & z0,
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::std::complex<T> const & z1 = ::std::complex<T>())
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: a(z0.real()),
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b(z0.imag()),
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c(z1.real()),
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d(z1.imag())
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{
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// nothing to do!
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}
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// UNtemplated copy constructor
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// (this is taken care of by the compiler itself)
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// templated copy constructor
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template<typename X>
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explicit quaternion(quaternion<X> const & a_recopier)
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: a(static_cast<T>(a_recopier.R_component_1())),
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b(static_cast<T>(a_recopier.R_component_2())),
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c(static_cast<T>(a_recopier.R_component_3())),
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d(static_cast<T>(a_recopier.R_component_4()))
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{
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// nothing to do!
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}
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// destructor
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// (this is taken care of by the compiler itself)
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// accessors
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//
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// Note: Like complex number, quaternions do have a meaningful notion of "real part",
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// but unlike them there is no meaningful notion of "imaginary part".
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// Instead there is an "unreal part" which itself is a quaternion, and usually
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// nothing simpler (as opposed to the complex number case).
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// However, for practicallity, there are accessors for the other components
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// (these are necessary for the templated copy constructor, for instance).
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BOOST_QUATERNION_ACCESSOR_GENERATOR(T)
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// assignment operators
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BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(T)
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// other assignment-related operators
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//
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// NOTE: Quaternion multiplication is *NOT* commutative;
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// symbolically, "q *= rhs;" means "q = q * rhs;"
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// and "q /= rhs;" means "q = q * inverse_of(rhs);"
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quaternion<T> & operator += (T const & rhs)
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{
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T at = a + rhs; // exception guard
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a = at;
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return(*this);
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}
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quaternion<T> & operator += (::std::complex<T> const & rhs)
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{
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T at = a + rhs.real(); // exception guard
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T bt = b + rhs.imag(); // exception guard
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a = at;
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b = bt;
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return(*this);
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}
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template<typename X>
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quaternion<T> & operator += (quaternion<X> const & rhs)
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{
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T at = a + static_cast<T>(rhs.R_component_1()); // exception guard
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T bt = b + static_cast<T>(rhs.R_component_2()); // exception guard
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T ct = c + static_cast<T>(rhs.R_component_3()); // exception guard
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T dt = d + static_cast<T>(rhs.R_component_4()); // exception guard
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a = at;
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b = bt;
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c = ct;
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d = dt;
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return(*this);
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}
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quaternion<T> & operator -= (T const & rhs)
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{
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T at = a - rhs; // exception guard
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a = at;
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return(*this);
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}
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quaternion<T> & operator -= (::std::complex<T> const & rhs)
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{
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T at = a - rhs.real(); // exception guard
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T bt = b - rhs.imag(); // exception guard
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a = at;
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b = bt;
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return(*this);
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}
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template<typename X>
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quaternion<T> & operator -= (quaternion<X> const & rhs)
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{
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T at = a - static_cast<T>(rhs.R_component_1()); // exception guard
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T bt = b - static_cast<T>(rhs.R_component_2()); // exception guard
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T ct = c - static_cast<T>(rhs.R_component_3()); // exception guard
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T dt = d - static_cast<T>(rhs.R_component_4()); // exception guard
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a = at;
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b = bt;
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c = ct;
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d = dt;
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return(*this);
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}
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quaternion<T> & operator *= (T const & rhs)
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{
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T at = a * rhs; // exception guard
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T bt = b * rhs; // exception guard
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T ct = c * rhs; // exception guard
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T dt = d * rhs; // exception guard
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309 |
|
williamr@2
|
310 |
a = at;
|
williamr@2
|
311 |
b = bt;
|
williamr@2
|
312 |
c = ct;
|
williamr@2
|
313 |
d = dt;
|
williamr@2
|
314 |
|
williamr@2
|
315 |
return(*this);
|
williamr@2
|
316 |
}
|
williamr@2
|
317 |
|
williamr@2
|
318 |
|
williamr@2
|
319 |
quaternion<T> & operator *= (::std::complex<T> const & rhs)
|
williamr@2
|
320 |
{
|
williamr@2
|
321 |
T ar = rhs.real();
|
williamr@2
|
322 |
T br = rhs.imag();
|
williamr@2
|
323 |
|
williamr@2
|
324 |
T at = +a*ar-b*br;
|
williamr@2
|
325 |
T bt = +a*br+b*ar;
|
williamr@2
|
326 |
T ct = +c*ar+d*br;
|
williamr@2
|
327 |
T dt = -c*br+d*ar;
|
williamr@2
|
328 |
|
williamr@2
|
329 |
a = at;
|
williamr@2
|
330 |
b = bt;
|
williamr@2
|
331 |
c = ct;
|
williamr@2
|
332 |
d = dt;
|
williamr@2
|
333 |
|
williamr@2
|
334 |
return(*this);
|
williamr@2
|
335 |
}
|
williamr@2
|
336 |
|
williamr@2
|
337 |
|
williamr@2
|
338 |
template<typename X>
|
williamr@2
|
339 |
quaternion<T> & operator *= (quaternion<X> const & rhs)
|
williamr@2
|
340 |
{
|
williamr@2
|
341 |
T ar = static_cast<T>(rhs.R_component_1());
|
williamr@2
|
342 |
T br = static_cast<T>(rhs.R_component_2());
|
williamr@2
|
343 |
T cr = static_cast<T>(rhs.R_component_3());
|
williamr@2
|
344 |
T dr = static_cast<T>(rhs.R_component_4());
|
williamr@2
|
345 |
|
williamr@2
|
346 |
T at = +a*ar-b*br-c*cr-d*dr;
|
williamr@2
|
347 |
T bt = +a*br+b*ar+c*dr-d*cr; //(a*br+ar*b)+(c*dr-cr*d);
|
williamr@2
|
348 |
T ct = +a*cr-b*dr+c*ar+d*br; //(a*cr+ar*c)+(d*br-dr*b);
|
williamr@2
|
349 |
T dt = +a*dr+b*cr-c*br+d*ar; //(a*dr+ar*d)+(b*cr-br*c);
|
williamr@2
|
350 |
|
williamr@2
|
351 |
a = at;
|
williamr@2
|
352 |
b = bt;
|
williamr@2
|
353 |
c = ct;
|
williamr@2
|
354 |
d = dt;
|
williamr@2
|
355 |
|
williamr@2
|
356 |
return(*this);
|
williamr@2
|
357 |
}
|
williamr@2
|
358 |
|
williamr@2
|
359 |
|
williamr@2
|
360 |
|
williamr@2
|
361 |
quaternion<T> & operator /= (T const & rhs)
|
williamr@2
|
362 |
{
|
williamr@2
|
363 |
T at = a / rhs; // exception guard
|
williamr@2
|
364 |
T bt = b / rhs; // exception guard
|
williamr@2
|
365 |
T ct = c / rhs; // exception guard
|
williamr@2
|
366 |
T dt = d / rhs; // exception guard
|
williamr@2
|
367 |
|
williamr@2
|
368 |
a = at;
|
williamr@2
|
369 |
b = bt;
|
williamr@2
|
370 |
c = ct;
|
williamr@2
|
371 |
d = dt;
|
williamr@2
|
372 |
|
williamr@2
|
373 |
return(*this);
|
williamr@2
|
374 |
}
|
williamr@2
|
375 |
|
williamr@2
|
376 |
|
williamr@2
|
377 |
quaternion<T> & operator /= (::std::complex<T> const & rhs)
|
williamr@2
|
378 |
{
|
williamr@2
|
379 |
T ar = rhs.real();
|
williamr@2
|
380 |
T br = rhs.imag();
|
williamr@2
|
381 |
|
williamr@2
|
382 |
T denominator = ar*ar+br*br;
|
williamr@2
|
383 |
|
williamr@2
|
384 |
T at = (+a*ar+b*br)/denominator; //(a*ar+b*br)/denominator;
|
williamr@2
|
385 |
T bt = (-a*br+b*ar)/denominator; //(ar*b-a*br)/denominator;
|
williamr@2
|
386 |
T ct = (+c*ar-d*br)/denominator; //(ar*c-d*br)/denominator;
|
williamr@2
|
387 |
T dt = (+c*br+d*ar)/denominator; //(ar*d+br*c)/denominator;
|
williamr@2
|
388 |
|
williamr@2
|
389 |
a = at;
|
williamr@2
|
390 |
b = bt;
|
williamr@2
|
391 |
c = ct;
|
williamr@2
|
392 |
d = dt;
|
williamr@2
|
393 |
|
williamr@2
|
394 |
return(*this);
|
williamr@2
|
395 |
}
|
williamr@2
|
396 |
|
williamr@2
|
397 |
|
williamr@2
|
398 |
template<typename X>
|
williamr@2
|
399 |
quaternion<T> & operator /= (quaternion<X> const & rhs)
|
williamr@2
|
400 |
{
|
williamr@2
|
401 |
T ar = static_cast<T>(rhs.R_component_1());
|
williamr@2
|
402 |
T br = static_cast<T>(rhs.R_component_2());
|
williamr@2
|
403 |
T cr = static_cast<T>(rhs.R_component_3());
|
williamr@2
|
404 |
T dr = static_cast<T>(rhs.R_component_4());
|
williamr@2
|
405 |
|
williamr@2
|
406 |
T denominator = ar*ar+br*br+cr*cr+dr*dr;
|
williamr@2
|
407 |
|
williamr@2
|
408 |
T at = (+a*ar+b*br+c*cr+d*dr)/denominator; //(a*ar+b*br+c*cr+d*dr)/denominator;
|
williamr@2
|
409 |
T bt = (-a*br+b*ar-c*dr+d*cr)/denominator; //((ar*b-a*br)+(cr*d-c*dr))/denominator;
|
williamr@2
|
410 |
T ct = (-a*cr+b*dr+c*ar-d*br)/denominator; //((ar*c-a*cr)+(dr*b-d*br))/denominator;
|
williamr@2
|
411 |
T dt = (-a*dr-b*cr+c*br+d*ar)/denominator; //((ar*d-a*dr)+(br*c-b*cr))/denominator;
|
williamr@2
|
412 |
|
williamr@2
|
413 |
a = at;
|
williamr@2
|
414 |
b = bt;
|
williamr@2
|
415 |
c = ct;
|
williamr@2
|
416 |
d = dt;
|
williamr@2
|
417 |
|
williamr@2
|
418 |
return(*this);
|
williamr@2
|
419 |
}
|
williamr@2
|
420 |
|
williamr@2
|
421 |
|
williamr@2
|
422 |
protected:
|
williamr@2
|
423 |
|
williamr@2
|
424 |
BOOST_QUATERNION_MEMBER_DATA_GENERATOR(T)
|
williamr@2
|
425 |
|
williamr@2
|
426 |
|
williamr@2
|
427 |
private:
|
williamr@2
|
428 |
|
williamr@2
|
429 |
};
|
williamr@2
|
430 |
|
williamr@2
|
431 |
|
williamr@2
|
432 |
// declaration of quaternion specialization
|
williamr@2
|
433 |
|
williamr@2
|
434 |
template<> class quaternion<float>;
|
williamr@2
|
435 |
template<> class quaternion<double>;
|
williamr@2
|
436 |
template<> class quaternion<long double>;
|
williamr@2
|
437 |
|
williamr@2
|
438 |
|
williamr@2
|
439 |
// helper templates for converting copy constructors (declaration)
|
williamr@2
|
440 |
|
williamr@2
|
441 |
namespace detail
|
williamr@2
|
442 |
{
|
williamr@2
|
443 |
|
williamr@2
|
444 |
template< typename T,
|
williamr@2
|
445 |
typename U
|
williamr@2
|
446 |
>
|
williamr@2
|
447 |
quaternion<T> quaternion_type_converter(quaternion<U> const & rhs);
|
williamr@2
|
448 |
}
|
williamr@2
|
449 |
|
williamr@2
|
450 |
|
williamr@2
|
451 |
// implementation of quaternion specialization
|
williamr@2
|
452 |
|
williamr@2
|
453 |
|
williamr@2
|
454 |
#define BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(type) \
|
williamr@2
|
455 |
explicit quaternion( type const & requested_a = static_cast<type>(0), \
|
williamr@2
|
456 |
type const & requested_b = static_cast<type>(0), \
|
williamr@2
|
457 |
type const & requested_c = static_cast<type>(0), \
|
williamr@2
|
458 |
type const & requested_d = static_cast<type>(0)) \
|
williamr@2
|
459 |
: a(requested_a), \
|
williamr@2
|
460 |
b(requested_b), \
|
williamr@2
|
461 |
c(requested_c), \
|
williamr@2
|
462 |
d(requested_d) \
|
williamr@2
|
463 |
{ \
|
williamr@2
|
464 |
} \
|
williamr@2
|
465 |
\
|
williamr@2
|
466 |
explicit quaternion( ::std::complex<type> const & z0, \
|
williamr@2
|
467 |
::std::complex<type> const & z1 = ::std::complex<type>()) \
|
williamr@2
|
468 |
: a(z0.real()), \
|
williamr@2
|
469 |
b(z0.imag()), \
|
williamr@2
|
470 |
c(z1.real()), \
|
williamr@2
|
471 |
d(z1.imag()) \
|
williamr@2
|
472 |
{ \
|
williamr@2
|
473 |
}
|
williamr@2
|
474 |
|
williamr@2
|
475 |
|
williamr@2
|
476 |
#define BOOST_QUATERNION_MEMBER_ADD_GENERATOR_1(type) \
|
williamr@2
|
477 |
quaternion<type> & operator += (type const & rhs) \
|
williamr@2
|
478 |
{ \
|
williamr@2
|
479 |
a += rhs; \
|
williamr@2
|
480 |
\
|
williamr@2
|
481 |
return(*this); \
|
williamr@2
|
482 |
}
|
williamr@2
|
483 |
|
williamr@2
|
484 |
#define BOOST_QUATERNION_MEMBER_ADD_GENERATOR_2(type) \
|
williamr@2
|
485 |
quaternion<type> & operator += (::std::complex<type> const & rhs) \
|
williamr@2
|
486 |
{ \
|
williamr@2
|
487 |
a += rhs.real(); \
|
williamr@2
|
488 |
b += rhs.imag(); \
|
williamr@2
|
489 |
\
|
williamr@2
|
490 |
return(*this); \
|
williamr@2
|
491 |
}
|
williamr@2
|
492 |
|
williamr@2
|
493 |
#define BOOST_QUATERNION_MEMBER_ADD_GENERATOR_3(type) \
|
williamr@2
|
494 |
template<typename X> \
|
williamr@2
|
495 |
quaternion<type> & operator += (quaternion<X> const & rhs) \
|
williamr@2
|
496 |
{ \
|
williamr@2
|
497 |
a += static_cast<type>(rhs.R_component_1()); \
|
williamr@2
|
498 |
b += static_cast<type>(rhs.R_component_2()); \
|
williamr@2
|
499 |
c += static_cast<type>(rhs.R_component_3()); \
|
williamr@2
|
500 |
d += static_cast<type>(rhs.R_component_4()); \
|
williamr@2
|
501 |
\
|
williamr@2
|
502 |
return(*this); \
|
williamr@2
|
503 |
}
|
williamr@2
|
504 |
|
williamr@2
|
505 |
#define BOOST_QUATERNION_MEMBER_SUB_GENERATOR_1(type) \
|
williamr@2
|
506 |
quaternion<type> & operator -= (type const & rhs) \
|
williamr@2
|
507 |
{ \
|
williamr@2
|
508 |
a -= rhs; \
|
williamr@2
|
509 |
\
|
williamr@2
|
510 |
return(*this); \
|
williamr@2
|
511 |
}
|
williamr@2
|
512 |
|
williamr@2
|
513 |
#define BOOST_QUATERNION_MEMBER_SUB_GENERATOR_2(type) \
|
williamr@2
|
514 |
quaternion<type> & operator -= (::std::complex<type> const & rhs) \
|
williamr@2
|
515 |
{ \
|
williamr@2
|
516 |
a -= rhs.real(); \
|
williamr@2
|
517 |
b -= rhs.imag(); \
|
williamr@2
|
518 |
\
|
williamr@2
|
519 |
return(*this); \
|
williamr@2
|
520 |
}
|
williamr@2
|
521 |
|
williamr@2
|
522 |
#define BOOST_QUATERNION_MEMBER_SUB_GENERATOR_3(type) \
|
williamr@2
|
523 |
template<typename X> \
|
williamr@2
|
524 |
quaternion<type> & operator -= (quaternion<X> const & rhs) \
|
williamr@2
|
525 |
{ \
|
williamr@2
|
526 |
a -= static_cast<type>(rhs.R_component_1()); \
|
williamr@2
|
527 |
b -= static_cast<type>(rhs.R_component_2()); \
|
williamr@2
|
528 |
c -= static_cast<type>(rhs.R_component_3()); \
|
williamr@2
|
529 |
d -= static_cast<type>(rhs.R_component_4()); \
|
williamr@2
|
530 |
\
|
williamr@2
|
531 |
return(*this); \
|
williamr@2
|
532 |
}
|
williamr@2
|
533 |
|
williamr@2
|
534 |
#define BOOST_QUATERNION_MEMBER_MUL_GENERATOR_1(type) \
|
williamr@2
|
535 |
quaternion<type> & operator *= (type const & rhs) \
|
williamr@2
|
536 |
{ \
|
williamr@2
|
537 |
a *= rhs; \
|
williamr@2
|
538 |
b *= rhs; \
|
williamr@2
|
539 |
c *= rhs; \
|
williamr@2
|
540 |
d *= rhs; \
|
williamr@2
|
541 |
\
|
williamr@2
|
542 |
return(*this); \
|
williamr@2
|
543 |
}
|
williamr@2
|
544 |
|
williamr@2
|
545 |
#define BOOST_QUATERNION_MEMBER_MUL_GENERATOR_2(type) \
|
williamr@2
|
546 |
quaternion<type> & operator *= (::std::complex<type> const & rhs) \
|
williamr@2
|
547 |
{ \
|
williamr@2
|
548 |
type ar = rhs.real(); \
|
williamr@2
|
549 |
type br = rhs.imag(); \
|
williamr@2
|
550 |
\
|
williamr@2
|
551 |
type at = +a*ar-b*br; \
|
williamr@2
|
552 |
type bt = +a*br+b*ar; \
|
williamr@2
|
553 |
type ct = +c*ar+d*br; \
|
williamr@2
|
554 |
type dt = -c*br+d*ar; \
|
williamr@2
|
555 |
\
|
williamr@2
|
556 |
a = at; \
|
williamr@2
|
557 |
b = bt; \
|
williamr@2
|
558 |
c = ct; \
|
williamr@2
|
559 |
d = dt; \
|
williamr@2
|
560 |
\
|
williamr@2
|
561 |
return(*this); \
|
williamr@2
|
562 |
}
|
williamr@2
|
563 |
|
williamr@2
|
564 |
#define BOOST_QUATERNION_MEMBER_MUL_GENERATOR_3(type) \
|
williamr@2
|
565 |
template<typename X> \
|
williamr@2
|
566 |
quaternion<type> & operator *= (quaternion<X> const & rhs) \
|
williamr@2
|
567 |
{ \
|
williamr@2
|
568 |
type ar = static_cast<type>(rhs.R_component_1()); \
|
williamr@2
|
569 |
type br = static_cast<type>(rhs.R_component_2()); \
|
williamr@2
|
570 |
type cr = static_cast<type>(rhs.R_component_3()); \
|
williamr@2
|
571 |
type dr = static_cast<type>(rhs.R_component_4()); \
|
williamr@2
|
572 |
\
|
williamr@2
|
573 |
type at = +a*ar-b*br-c*cr-d*dr; \
|
williamr@2
|
574 |
type bt = +a*br+b*ar+c*dr-d*cr; \
|
williamr@2
|
575 |
type ct = +a*cr-b*dr+c*ar+d*br; \
|
williamr@2
|
576 |
type dt = +a*dr+b*cr-c*br+d*ar; \
|
williamr@2
|
577 |
\
|
williamr@2
|
578 |
a = at; \
|
williamr@2
|
579 |
b = bt; \
|
williamr@2
|
580 |
c = ct; \
|
williamr@2
|
581 |
d = dt; \
|
williamr@2
|
582 |
\
|
williamr@2
|
583 |
return(*this); \
|
williamr@2
|
584 |
}
|
williamr@2
|
585 |
|
williamr@2
|
586 |
// There is quite a lot of repetition in the code below. This is intentional.
|
williamr@2
|
587 |
// The last conditional block is the normal form, and the others merely
|
williamr@2
|
588 |
// consist of workarounds for various compiler deficiencies. Hopefuly, when
|
williamr@2
|
589 |
// more compilers are conformant and we can retire support for those that are
|
williamr@2
|
590 |
// not, we will be able to remove the clutter. This is makes the situation
|
williamr@2
|
591 |
// (painfully) explicit.
|
williamr@2
|
592 |
|
williamr@2
|
593 |
#define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_1(type) \
|
williamr@2
|
594 |
quaternion<type> & operator /= (type const & rhs) \
|
williamr@2
|
595 |
{ \
|
williamr@2
|
596 |
a /= rhs; \
|
williamr@2
|
597 |
b /= rhs; \
|
williamr@2
|
598 |
c /= rhs; \
|
williamr@2
|
599 |
d /= rhs; \
|
williamr@2
|
600 |
\
|
williamr@2
|
601 |
return(*this); \
|
williamr@2
|
602 |
}
|
williamr@2
|
603 |
|
williamr@2
|
604 |
#if defined(__GNUC__) && (__GNUC__ < 3)
|
williamr@2
|
605 |
#define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \
|
williamr@2
|
606 |
quaternion<type> & operator /= (::std::complex<type> const & rhs) \
|
williamr@2
|
607 |
{ \
|
williamr@2
|
608 |
using ::std::valarray; \
|
williamr@2
|
609 |
\
|
williamr@2
|
610 |
valarray<type> tr(2); \
|
williamr@2
|
611 |
\
|
williamr@2
|
612 |
tr[0] = rhs.real(); \
|
williamr@2
|
613 |
tr[1] = rhs.imag(); \
|
williamr@2
|
614 |
\
|
williamr@2
|
615 |
type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)(); \
|
williamr@2
|
616 |
\
|
williamr@2
|
617 |
tr *= mixam; \
|
williamr@2
|
618 |
\
|
williamr@2
|
619 |
valarray<type> tt(4); \
|
williamr@2
|
620 |
\
|
williamr@2
|
621 |
tt[0] = +a*tr[0]+b*tr[1]; \
|
williamr@2
|
622 |
tt[1] = -a*tr[1]+b*tr[0]; \
|
williamr@2
|
623 |
tt[2] = +c*tr[0]-d*tr[1]; \
|
williamr@2
|
624 |
tt[3] = +c*tr[1]+d*tr[0]; \
|
williamr@2
|
625 |
\
|
williamr@2
|
626 |
tr *= tr; \
|
williamr@2
|
627 |
\
|
williamr@2
|
628 |
tt *= (mixam/tr.sum()); \
|
williamr@2
|
629 |
\
|
williamr@2
|
630 |
a = tt[0]; \
|
williamr@2
|
631 |
b = tt[1]; \
|
williamr@2
|
632 |
c = tt[2]; \
|
williamr@2
|
633 |
d = tt[3]; \
|
williamr@2
|
634 |
\
|
williamr@2
|
635 |
return(*this); \
|
williamr@2
|
636 |
}
|
williamr@2
|
637 |
#elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
|
williamr@2
|
638 |
#define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \
|
williamr@2
|
639 |
quaternion<type> & operator /= (::std::complex<type> const & rhs) \
|
williamr@2
|
640 |
{ \
|
williamr@2
|
641 |
using ::std::valarray; \
|
williamr@2
|
642 |
using ::std::abs; \
|
williamr@2
|
643 |
\
|
williamr@2
|
644 |
valarray<type> tr(2); \
|
williamr@2
|
645 |
\
|
williamr@2
|
646 |
tr[0] = rhs.real(); \
|
williamr@2
|
647 |
tr[1] = rhs.imag(); \
|
williamr@2
|
648 |
\
|
williamr@2
|
649 |
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
|
williamr@2
|
650 |
\
|
williamr@2
|
651 |
tr *= mixam; \
|
williamr@2
|
652 |
\
|
williamr@2
|
653 |
valarray<type> tt(4); \
|
williamr@2
|
654 |
\
|
williamr@2
|
655 |
tt[0] = +a*tr[0]+b*tr[1]; \
|
williamr@2
|
656 |
tt[1] = -a*tr[1]+b*tr[0]; \
|
williamr@2
|
657 |
tt[2] = +c*tr[0]-d*tr[1]; \
|
williamr@2
|
658 |
tt[3] = +c*tr[1]+d*tr[0]; \
|
williamr@2
|
659 |
\
|
williamr@2
|
660 |
tr *= tr; \
|
williamr@2
|
661 |
\
|
williamr@2
|
662 |
tt *= (mixam/tr.sum()); \
|
williamr@2
|
663 |
\
|
williamr@2
|
664 |
a = tt[0]; \
|
williamr@2
|
665 |
b = tt[1]; \
|
williamr@2
|
666 |
c = tt[2]; \
|
williamr@2
|
667 |
d = tt[3]; \
|
williamr@2
|
668 |
\
|
williamr@2
|
669 |
return(*this); \
|
williamr@2
|
670 |
}
|
williamr@2
|
671 |
#else
|
williamr@2
|
672 |
#define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \
|
williamr@2
|
673 |
quaternion<type> & operator /= (::std::complex<type> const & rhs) \
|
williamr@2
|
674 |
{ \
|
williamr@2
|
675 |
using ::std::valarray; \
|
williamr@2
|
676 |
\
|
williamr@2
|
677 |
valarray<type> tr(2); \
|
williamr@2
|
678 |
\
|
williamr@2
|
679 |
tr[0] = rhs.real(); \
|
williamr@2
|
680 |
tr[1] = rhs.imag(); \
|
williamr@2
|
681 |
\
|
williamr@2
|
682 |
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
|
williamr@2
|
683 |
\
|
williamr@2
|
684 |
tr *= mixam; \
|
williamr@2
|
685 |
\
|
williamr@2
|
686 |
valarray<type> tt(4); \
|
williamr@2
|
687 |
\
|
williamr@2
|
688 |
tt[0] = +a*tr[0]+b*tr[1]; \
|
williamr@2
|
689 |
tt[1] = -a*tr[1]+b*tr[0]; \
|
williamr@2
|
690 |
tt[2] = +c*tr[0]-d*tr[1]; \
|
williamr@2
|
691 |
tt[3] = +c*tr[1]+d*tr[0]; \
|
williamr@2
|
692 |
\
|
williamr@2
|
693 |
tr *= tr; \
|
williamr@2
|
694 |
\
|
williamr@2
|
695 |
tt *= (mixam/tr.sum()); \
|
williamr@2
|
696 |
\
|
williamr@2
|
697 |
a = tt[0]; \
|
williamr@2
|
698 |
b = tt[1]; \
|
williamr@2
|
699 |
c = tt[2]; \
|
williamr@2
|
700 |
d = tt[3]; \
|
williamr@2
|
701 |
\
|
williamr@2
|
702 |
return(*this); \
|
williamr@2
|
703 |
}
|
williamr@2
|
704 |
#endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
williamr@2
|
705 |
|
williamr@2
|
706 |
#if defined(__GNUC__) && (__GNUC__ < 3)
|
williamr@2
|
707 |
#define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type) \
|
williamr@2
|
708 |
template<typename X> \
|
williamr@2
|
709 |
quaternion<type> & operator /= (quaternion<X> const & rhs) \
|
williamr@2
|
710 |
{ \
|
williamr@2
|
711 |
using ::std::valarray; \
|
williamr@2
|
712 |
\
|
williamr@2
|
713 |
valarray<type> tr(4); \
|
williamr@2
|
714 |
\
|
williamr@2
|
715 |
tr[0] = static_cast<type>(rhs.R_component_1()); \
|
williamr@2
|
716 |
tr[1] = static_cast<type>(rhs.R_component_2()); \
|
williamr@2
|
717 |
tr[2] = static_cast<type>(rhs.R_component_3()); \
|
williamr@2
|
718 |
tr[3] = static_cast<type>(rhs.R_component_4()); \
|
williamr@2
|
719 |
\
|
williamr@2
|
720 |
type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)(); \
|
williamr@2
|
721 |
\
|
williamr@2
|
722 |
tr *= mixam; \
|
williamr@2
|
723 |
\
|
williamr@2
|
724 |
valarray<type> tt(4); \
|
williamr@2
|
725 |
\
|
williamr@2
|
726 |
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
|
williamr@2
|
727 |
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
|
williamr@2
|
728 |
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
|
williamr@2
|
729 |
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
|
williamr@2
|
730 |
\
|
williamr@2
|
731 |
tr *= tr; \
|
williamr@2
|
732 |
\
|
williamr@2
|
733 |
tt *= (mixam/tr.sum()); \
|
williamr@2
|
734 |
\
|
williamr@2
|
735 |
a = tt[0]; \
|
williamr@2
|
736 |
b = tt[1]; \
|
williamr@2
|
737 |
c = tt[2]; \
|
williamr@2
|
738 |
d = tt[3]; \
|
williamr@2
|
739 |
\
|
williamr@2
|
740 |
return(*this); \
|
williamr@2
|
741 |
}
|
williamr@2
|
742 |
#elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
|
williamr@2
|
743 |
#define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type) \
|
williamr@2
|
744 |
template<typename X> \
|
williamr@2
|
745 |
quaternion<type> & operator /= (quaternion<X> const & rhs) \
|
williamr@2
|
746 |
{ \
|
williamr@2
|
747 |
using ::std::valarray; \
|
williamr@2
|
748 |
using ::std::abs; \
|
williamr@2
|
749 |
\
|
williamr@2
|
750 |
valarray<type> tr(4); \
|
williamr@2
|
751 |
\
|
williamr@2
|
752 |
tr[0] = static_cast<type>(rhs.R_component_1()); \
|
williamr@2
|
753 |
tr[1] = static_cast<type>(rhs.R_component_2()); \
|
williamr@2
|
754 |
tr[2] = static_cast<type>(rhs.R_component_3()); \
|
williamr@2
|
755 |
tr[3] = static_cast<type>(rhs.R_component_4()); \
|
williamr@2
|
756 |
\
|
williamr@2
|
757 |
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
|
williamr@2
|
758 |
\
|
williamr@2
|
759 |
tr *= mixam; \
|
williamr@2
|
760 |
\
|
williamr@2
|
761 |
valarray<type> tt(4); \
|
williamr@2
|
762 |
\
|
williamr@2
|
763 |
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
|
williamr@2
|
764 |
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
|
williamr@2
|
765 |
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
|
williamr@2
|
766 |
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
|
williamr@2
|
767 |
\
|
williamr@2
|
768 |
tr *= tr; \
|
williamr@2
|
769 |
\
|
williamr@2
|
770 |
tt *= (mixam/tr.sum()); \
|
williamr@2
|
771 |
\
|
williamr@2
|
772 |
a = tt[0]; \
|
williamr@2
|
773 |
b = tt[1]; \
|
williamr@2
|
774 |
c = tt[2]; \
|
williamr@2
|
775 |
d = tt[3]; \
|
williamr@2
|
776 |
\
|
williamr@2
|
777 |
return(*this); \
|
williamr@2
|
778 |
}
|
williamr@2
|
779 |
#else
|
williamr@2
|
780 |
#define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type) \
|
williamr@2
|
781 |
template<typename X> \
|
williamr@2
|
782 |
quaternion<type> & operator /= (quaternion<X> const & rhs) \
|
williamr@2
|
783 |
{ \
|
williamr@2
|
784 |
using ::std::valarray; \
|
williamr@2
|
785 |
\
|
williamr@2
|
786 |
valarray<type> tr(4); \
|
williamr@2
|
787 |
\
|
williamr@2
|
788 |
tr[0] = static_cast<type>(rhs.R_component_1()); \
|
williamr@2
|
789 |
tr[1] = static_cast<type>(rhs.R_component_2()); \
|
williamr@2
|
790 |
tr[2] = static_cast<type>(rhs.R_component_3()); \
|
williamr@2
|
791 |
tr[3] = static_cast<type>(rhs.R_component_4()); \
|
williamr@2
|
792 |
\
|
williamr@2
|
793 |
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
|
williamr@2
|
794 |
\
|
williamr@2
|
795 |
tr *= mixam; \
|
williamr@2
|
796 |
\
|
williamr@2
|
797 |
valarray<type> tt(4); \
|
williamr@2
|
798 |
\
|
williamr@2
|
799 |
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
|
williamr@2
|
800 |
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
|
williamr@2
|
801 |
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
|
williamr@2
|
802 |
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
|
williamr@2
|
803 |
\
|
williamr@2
|
804 |
tr *= tr; \
|
williamr@2
|
805 |
\
|
williamr@2
|
806 |
tt *= (mixam/tr.sum()); \
|
williamr@2
|
807 |
\
|
williamr@2
|
808 |
a = tt[0]; \
|
williamr@2
|
809 |
b = tt[1]; \
|
williamr@2
|
810 |
c = tt[2]; \
|
williamr@2
|
811 |
d = tt[3]; \
|
williamr@2
|
812 |
\
|
williamr@2
|
813 |
return(*this); \
|
williamr@2
|
814 |
}
|
williamr@2
|
815 |
#endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
williamr@2
|
816 |
|
williamr@2
|
817 |
#define BOOST_QUATERNION_MEMBER_ADD_GENERATOR(type) \
|
williamr@2
|
818 |
BOOST_QUATERNION_MEMBER_ADD_GENERATOR_1(type) \
|
williamr@2
|
819 |
BOOST_QUATERNION_MEMBER_ADD_GENERATOR_2(type) \
|
williamr@2
|
820 |
BOOST_QUATERNION_MEMBER_ADD_GENERATOR_3(type)
|
williamr@2
|
821 |
|
williamr@2
|
822 |
#define BOOST_QUATERNION_MEMBER_SUB_GENERATOR(type) \
|
williamr@2
|
823 |
BOOST_QUATERNION_MEMBER_SUB_GENERATOR_1(type) \
|
williamr@2
|
824 |
BOOST_QUATERNION_MEMBER_SUB_GENERATOR_2(type) \
|
williamr@2
|
825 |
BOOST_QUATERNION_MEMBER_SUB_GENERATOR_3(type)
|
williamr@2
|
826 |
|
williamr@2
|
827 |
#define BOOST_QUATERNION_MEMBER_MUL_GENERATOR(type) \
|
williamr@2
|
828 |
BOOST_QUATERNION_MEMBER_MUL_GENERATOR_1(type) \
|
williamr@2
|
829 |
BOOST_QUATERNION_MEMBER_MUL_GENERATOR_2(type) \
|
williamr@2
|
830 |
BOOST_QUATERNION_MEMBER_MUL_GENERATOR_3(type)
|
williamr@2
|
831 |
|
williamr@2
|
832 |
#define BOOST_QUATERNION_MEMBER_DIV_GENERATOR(type) \
|
williamr@2
|
833 |
BOOST_QUATERNION_MEMBER_DIV_GENERATOR_1(type) \
|
williamr@2
|
834 |
BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \
|
williamr@2
|
835 |
BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type)
|
williamr@2
|
836 |
|
williamr@2
|
837 |
#define BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(type) \
|
williamr@2
|
838 |
BOOST_QUATERNION_MEMBER_ADD_GENERATOR(type) \
|
williamr@2
|
839 |
BOOST_QUATERNION_MEMBER_SUB_GENERATOR(type) \
|
williamr@2
|
840 |
BOOST_QUATERNION_MEMBER_MUL_GENERATOR(type) \
|
williamr@2
|
841 |
BOOST_QUATERNION_MEMBER_DIV_GENERATOR(type)
|
williamr@2
|
842 |
|
williamr@2
|
843 |
|
williamr@2
|
844 |
template<>
|
williamr@2
|
845 |
class quaternion<float>
|
williamr@2
|
846 |
{
|
williamr@2
|
847 |
public:
|
williamr@2
|
848 |
|
williamr@2
|
849 |
typedef float value_type;
|
williamr@2
|
850 |
|
williamr@2
|
851 |
BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(float)
|
williamr@2
|
852 |
|
williamr@2
|
853 |
// UNtemplated copy constructor
|
williamr@2
|
854 |
// (this is taken care of by the compiler itself)
|
williamr@2
|
855 |
|
williamr@2
|
856 |
// explicit copy constructors (precision-loosing converters)
|
williamr@2
|
857 |
|
williamr@2
|
858 |
explicit quaternion(quaternion<double> const & a_recopier)
|
williamr@2
|
859 |
{
|
williamr@2
|
860 |
*this = detail::quaternion_type_converter<float, double>(a_recopier);
|
williamr@2
|
861 |
}
|
williamr@2
|
862 |
|
williamr@2
|
863 |
explicit quaternion(quaternion<long double> const & a_recopier)
|
williamr@2
|
864 |
{
|
williamr@2
|
865 |
*this = detail::quaternion_type_converter<float, long double>(a_recopier);
|
williamr@2
|
866 |
}
|
williamr@2
|
867 |
|
williamr@2
|
868 |
// destructor
|
williamr@2
|
869 |
// (this is taken care of by the compiler itself)
|
williamr@2
|
870 |
|
williamr@2
|
871 |
// accessors
|
williamr@2
|
872 |
//
|
williamr@2
|
873 |
// Note: Like complex number, quaternions do have a meaningful notion of "real part",
|
williamr@2
|
874 |
// but unlike them there is no meaningful notion of "imaginary part".
|
williamr@2
|
875 |
// Instead there is an "unreal part" which itself is a quaternion, and usually
|
williamr@2
|
876 |
// nothing simpler (as opposed to the complex number case).
|
williamr@2
|
877 |
// However, for practicallity, there are accessors for the other components
|
williamr@2
|
878 |
// (these are necessary for the templated copy constructor, for instance).
|
williamr@2
|
879 |
|
williamr@2
|
880 |
BOOST_QUATERNION_ACCESSOR_GENERATOR(float)
|
williamr@2
|
881 |
|
williamr@2
|
882 |
// assignment operators
|
williamr@2
|
883 |
|
williamr@2
|
884 |
BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(float)
|
williamr@2
|
885 |
|
williamr@2
|
886 |
// other assignment-related operators
|
williamr@2
|
887 |
//
|
williamr@2
|
888 |
// NOTE: Quaternion multiplication is *NOT* commutative;
|
williamr@2
|
889 |
// symbolically, "q *= rhs;" means "q = q * rhs;"
|
williamr@2
|
890 |
// and "q /= rhs;" means "q = q * inverse_of(rhs);"
|
williamr@2
|
891 |
|
williamr@2
|
892 |
BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(float)
|
williamr@2
|
893 |
|
williamr@2
|
894 |
|
williamr@2
|
895 |
protected:
|
williamr@2
|
896 |
|
williamr@2
|
897 |
BOOST_QUATERNION_MEMBER_DATA_GENERATOR(float)
|
williamr@2
|
898 |
|
williamr@2
|
899 |
|
williamr@2
|
900 |
private:
|
williamr@2
|
901 |
|
williamr@2
|
902 |
};
|
williamr@2
|
903 |
|
williamr@2
|
904 |
|
williamr@2
|
905 |
template<>
|
williamr@2
|
906 |
class quaternion<double>
|
williamr@2
|
907 |
{
|
williamr@2
|
908 |
public:
|
williamr@2
|
909 |
|
williamr@2
|
910 |
typedef double value_type;
|
williamr@2
|
911 |
|
williamr@2
|
912 |
BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(double)
|
williamr@2
|
913 |
|
williamr@2
|
914 |
// UNtemplated copy constructor
|
williamr@2
|
915 |
// (this is taken care of by the compiler itself)
|
williamr@2
|
916 |
|
williamr@2
|
917 |
// converting copy constructor
|
williamr@2
|
918 |
|
williamr@2
|
919 |
explicit quaternion(quaternion<float> const & a_recopier)
|
williamr@2
|
920 |
{
|
williamr@2
|
921 |
*this = detail::quaternion_type_converter<double, float>(a_recopier);
|
williamr@2
|
922 |
}
|
williamr@2
|
923 |
|
williamr@2
|
924 |
// explicit copy constructors (precision-loosing converters)
|
williamr@2
|
925 |
|
williamr@2
|
926 |
explicit quaternion(quaternion<long double> const & a_recopier)
|
williamr@2
|
927 |
{
|
williamr@2
|
928 |
*this = detail::quaternion_type_converter<double, long double>(a_recopier);
|
williamr@2
|
929 |
}
|
williamr@2
|
930 |
|
williamr@2
|
931 |
// destructor
|
williamr@2
|
932 |
// (this is taken care of by the compiler itself)
|
williamr@2
|
933 |
|
williamr@2
|
934 |
// accessors
|
williamr@2
|
935 |
//
|
williamr@2
|
936 |
// Note: Like complex number, quaternions do have a meaningful notion of "real part",
|
williamr@2
|
937 |
// but unlike them there is no meaningful notion of "imaginary part".
|
williamr@2
|
938 |
// Instead there is an "unreal part" which itself is a quaternion, and usually
|
williamr@2
|
939 |
// nothing simpler (as opposed to the complex number case).
|
williamr@2
|
940 |
// However, for practicallity, there are accessors for the other components
|
williamr@2
|
941 |
// (these are necessary for the templated copy constructor, for instance).
|
williamr@2
|
942 |
|
williamr@2
|
943 |
BOOST_QUATERNION_ACCESSOR_GENERATOR(double)
|
williamr@2
|
944 |
|
williamr@2
|
945 |
// assignment operators
|
williamr@2
|
946 |
|
williamr@2
|
947 |
BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(double)
|
williamr@2
|
948 |
|
williamr@2
|
949 |
// other assignment-related operators
|
williamr@2
|
950 |
//
|
williamr@2
|
951 |
// NOTE: Quaternion multiplication is *NOT* commutative;
|
williamr@2
|
952 |
// symbolically, "q *= rhs;" means "q = q * rhs;"
|
williamr@2
|
953 |
// and "q /= rhs;" means "q = q * inverse_of(rhs);"
|
williamr@2
|
954 |
|
williamr@2
|
955 |
BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(double)
|
williamr@2
|
956 |
|
williamr@2
|
957 |
|
williamr@2
|
958 |
protected:
|
williamr@2
|
959 |
|
williamr@2
|
960 |
BOOST_QUATERNION_MEMBER_DATA_GENERATOR(double)
|
williamr@2
|
961 |
|
williamr@2
|
962 |
|
williamr@2
|
963 |
private:
|
williamr@2
|
964 |
|
williamr@2
|
965 |
};
|
williamr@2
|
966 |
|
williamr@2
|
967 |
|
williamr@2
|
968 |
template<>
|
williamr@2
|
969 |
class quaternion<long double>
|
williamr@2
|
970 |
{
|
williamr@2
|
971 |
public:
|
williamr@2
|
972 |
|
williamr@2
|
973 |
typedef long double value_type;
|
williamr@2
|
974 |
|
williamr@2
|
975 |
BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(long double)
|
williamr@2
|
976 |
|
williamr@2
|
977 |
// UNtemplated copy constructor
|
williamr@2
|
978 |
// (this is taken care of by the compiler itself)
|
williamr@2
|
979 |
|
williamr@2
|
980 |
// converting copy constructors
|
williamr@2
|
981 |
|
williamr@2
|
982 |
explicit quaternion(quaternion<float> const & a_recopier)
|
williamr@2
|
983 |
{
|
williamr@2
|
984 |
*this = detail::quaternion_type_converter<long double, float>(a_recopier);
|
williamr@2
|
985 |
}
|
williamr@2
|
986 |
|
williamr@2
|
987 |
explicit quaternion(quaternion<double> const & a_recopier)
|
williamr@2
|
988 |
{
|
williamr@2
|
989 |
*this = detail::quaternion_type_converter<long double, double>(a_recopier);
|
williamr@2
|
990 |
}
|
williamr@2
|
991 |
|
williamr@2
|
992 |
// destructor
|
williamr@2
|
993 |
// (this is taken care of by the compiler itself)
|
williamr@2
|
994 |
|
williamr@2
|
995 |
// accessors
|
williamr@2
|
996 |
//
|
williamr@2
|
997 |
// Note: Like complex number, quaternions do have a meaningful notion of "real part",
|
williamr@2
|
998 |
// but unlike them there is no meaningful notion of "imaginary part".
|
williamr@2
|
999 |
// Instead there is an "unreal part" which itself is a quaternion, and usually
|
williamr@2
|
1000 |
// nothing simpler (as opposed to the complex number case).
|
williamr@2
|
1001 |
// However, for practicallity, there are accessors for the other components
|
williamr@2
|
1002 |
// (these are necessary for the templated copy constructor, for instance).
|
williamr@2
|
1003 |
|
williamr@2
|
1004 |
BOOST_QUATERNION_ACCESSOR_GENERATOR(long double)
|
williamr@2
|
1005 |
|
williamr@2
|
1006 |
// assignment operators
|
williamr@2
|
1007 |
|
williamr@2
|
1008 |
BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(long double)
|
williamr@2
|
1009 |
|
williamr@2
|
1010 |
// other assignment-related operators
|
williamr@2
|
1011 |
//
|
williamr@2
|
1012 |
// NOTE: Quaternion multiplication is *NOT* commutative;
|
williamr@2
|
1013 |
// symbolically, "q *= rhs;" means "q = q * rhs;"
|
williamr@2
|
1014 |
// and "q /= rhs;" means "q = q * inverse_of(rhs);"
|
williamr@2
|
1015 |
|
williamr@2
|
1016 |
BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(long double)
|
williamr@2
|
1017 |
|
williamr@2
|
1018 |
|
williamr@2
|
1019 |
protected:
|
williamr@2
|
1020 |
|
williamr@2
|
1021 |
BOOST_QUATERNION_MEMBER_DATA_GENERATOR(long double)
|
williamr@2
|
1022 |
|
williamr@2
|
1023 |
|
williamr@2
|
1024 |
private:
|
williamr@2
|
1025 |
|
williamr@2
|
1026 |
};
|
williamr@2
|
1027 |
|
williamr@2
|
1028 |
|
williamr@2
|
1029 |
#undef BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR
|
williamr@2
|
1030 |
#undef BOOST_QUATERNION_MEMBER_ADD_GENERATOR
|
williamr@2
|
1031 |
#undef BOOST_QUATERNION_MEMBER_SUB_GENERATOR
|
williamr@2
|
1032 |
#undef BOOST_QUATERNION_MEMBER_MUL_GENERATOR
|
williamr@2
|
1033 |
#undef BOOST_QUATERNION_MEMBER_DIV_GENERATOR
|
williamr@2
|
1034 |
#undef BOOST_QUATERNION_MEMBER_ADD_GENERATOR_1
|
williamr@2
|
1035 |
#undef BOOST_QUATERNION_MEMBER_ADD_GENERATOR_2
|
williamr@2
|
1036 |
#undef BOOST_QUATERNION_MEMBER_ADD_GENERATOR_3
|
williamr@2
|
1037 |
#undef BOOST_QUATERNION_MEMBER_SUB_GENERATOR_1
|
williamr@2
|
1038 |
#undef BOOST_QUATERNION_MEMBER_SUB_GENERATOR_2
|
williamr@2
|
1039 |
#undef BOOST_QUATERNION_MEMBER_SUB_GENERATOR_3
|
williamr@2
|
1040 |
#undef BOOST_QUATERNION_MEMBER_MUL_GENERATOR_1
|
williamr@2
|
1041 |
#undef BOOST_QUATERNION_MEMBER_MUL_GENERATOR_2
|
williamr@2
|
1042 |
#undef BOOST_QUATERNION_MEMBER_MUL_GENERATOR_3
|
williamr@2
|
1043 |
#undef BOOST_QUATERNION_MEMBER_DIV_GENERATOR_1
|
williamr@2
|
1044 |
#undef BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2
|
williamr@2
|
1045 |
#undef BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3
|
williamr@2
|
1046 |
|
williamr@2
|
1047 |
#undef BOOST_QUATERNION_CONSTRUCTOR_GENERATOR
|
williamr@2
|
1048 |
|
williamr@2
|
1049 |
|
williamr@2
|
1050 |
#undef BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR
|
williamr@2
|
1051 |
|
williamr@2
|
1052 |
#undef BOOST_QUATERNION_MEMBER_DATA_GENERATOR
|
williamr@2
|
1053 |
|
williamr@2
|
1054 |
#undef BOOST_QUATERNION_ACCESSOR_GENERATOR
|
williamr@2
|
1055 |
|
williamr@2
|
1056 |
|
williamr@2
|
1057 |
// operators
|
williamr@2
|
1058 |
|
williamr@2
|
1059 |
#define BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op) \
|
williamr@2
|
1060 |
{ \
|
williamr@2
|
1061 |
quaternion<T> res(lhs); \
|
williamr@2
|
1062 |
res op##= rhs; \
|
williamr@2
|
1063 |
return(res); \
|
williamr@2
|
1064 |
}
|
williamr@2
|
1065 |
|
williamr@2
|
1066 |
#define BOOST_QUATERNION_OPERATOR_GENERATOR_1_L(op) \
|
williamr@2
|
1067 |
template<typename T> \
|
williamr@2
|
1068 |
inline quaternion<T> operator op (T const & lhs, quaternion<T> const & rhs) \
|
williamr@2
|
1069 |
BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op)
|
williamr@2
|
1070 |
|
williamr@2
|
1071 |
#define BOOST_QUATERNION_OPERATOR_GENERATOR_1_R(op) \
|
williamr@2
|
1072 |
template<typename T> \
|
williamr@2
|
1073 |
inline quaternion<T> operator op (quaternion<T> const & lhs, T const & rhs) \
|
williamr@2
|
1074 |
BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op)
|
williamr@2
|
1075 |
|
williamr@2
|
1076 |
#define BOOST_QUATERNION_OPERATOR_GENERATOR_2_L(op) \
|
williamr@2
|
1077 |
template<typename T> \
|
williamr@2
|
1078 |
inline quaternion<T> operator op (::std::complex<T> const & lhs, quaternion<T> const & rhs) \
|
williamr@2
|
1079 |
BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op)
|
williamr@2
|
1080 |
|
williamr@2
|
1081 |
#define BOOST_QUATERNION_OPERATOR_GENERATOR_2_R(op) \
|
williamr@2
|
1082 |
template<typename T> \
|
williamr@2
|
1083 |
inline quaternion<T> operator op (quaternion<T> const & lhs, ::std::complex<T> const & rhs) \
|
williamr@2
|
1084 |
BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op)
|
williamr@2
|
1085 |
|
williamr@2
|
1086 |
#define BOOST_QUATERNION_OPERATOR_GENERATOR_3(op) \
|
williamr@2
|
1087 |
template<typename T> \
|
williamr@2
|
1088 |
inline quaternion<T> operator op (quaternion<T> const & lhs, quaternion<T> const & rhs) \
|
williamr@2
|
1089 |
BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op)
|
williamr@2
|
1090 |
|
williamr@2
|
1091 |
#define BOOST_QUATERNION_OPERATOR_GENERATOR(op) \
|
williamr@2
|
1092 |
BOOST_QUATERNION_OPERATOR_GENERATOR_1_L(op) \
|
williamr@2
|
1093 |
BOOST_QUATERNION_OPERATOR_GENERATOR_1_R(op) \
|
williamr@2
|
1094 |
BOOST_QUATERNION_OPERATOR_GENERATOR_2_L(op) \
|
williamr@2
|
1095 |
BOOST_QUATERNION_OPERATOR_GENERATOR_2_R(op) \
|
williamr@2
|
1096 |
BOOST_QUATERNION_OPERATOR_GENERATOR_3(op)
|
williamr@2
|
1097 |
|
williamr@2
|
1098 |
|
williamr@2
|
1099 |
BOOST_QUATERNION_OPERATOR_GENERATOR(+)
|
williamr@2
|
1100 |
BOOST_QUATERNION_OPERATOR_GENERATOR(-)
|
williamr@2
|
1101 |
BOOST_QUATERNION_OPERATOR_GENERATOR(*)
|
williamr@2
|
1102 |
BOOST_QUATERNION_OPERATOR_GENERATOR(/)
|
williamr@2
|
1103 |
|
williamr@2
|
1104 |
|
williamr@2
|
1105 |
#undef BOOST_QUATERNION_OPERATOR_GENERATOR
|
williamr@2
|
1106 |
|
williamr@2
|
1107 |
#undef BOOST_QUATERNION_OPERATOR_GENERATOR_1_L
|
williamr@2
|
1108 |
#undef BOOST_QUATERNION_OPERATOR_GENERATOR_1_R
|
williamr@2
|
1109 |
#undef BOOST_QUATERNION_OPERATOR_GENERATOR_2_L
|
williamr@2
|
1110 |
#undef BOOST_QUATERNION_OPERATOR_GENERATOR_2_R
|
williamr@2
|
1111 |
#undef BOOST_QUATERNION_OPERATOR_GENERATOR_3
|
williamr@2
|
1112 |
|
williamr@2
|
1113 |
#undef BOOST_QUATERNION_OPERATOR_GENERATOR_BODY
|
williamr@2
|
1114 |
|
williamr@2
|
1115 |
|
williamr@2
|
1116 |
template<typename T>
|
williamr@2
|
1117 |
inline quaternion<T> operator + (quaternion<T> const & q)
|
williamr@2
|
1118 |
{
|
williamr@2
|
1119 |
return(q);
|
williamr@2
|
1120 |
}
|
williamr@2
|
1121 |
|
williamr@2
|
1122 |
|
williamr@2
|
1123 |
template<typename T>
|
williamr@2
|
1124 |
inline quaternion<T> operator - (quaternion<T> const & q)
|
williamr@2
|
1125 |
{
|
williamr@2
|
1126 |
return(quaternion<T>(-q.R_component_1(),-q.R_component_2(),-q.R_component_3(),-q.R_component_4()));
|
williamr@2
|
1127 |
}
|
williamr@2
|
1128 |
|
williamr@2
|
1129 |
|
williamr@2
|
1130 |
template<typename T>
|
williamr@2
|
1131 |
inline bool operator == (T const & lhs, quaternion<T> const & rhs)
|
williamr@2
|
1132 |
{
|
williamr@2
|
1133 |
return (
|
williamr@2
|
1134 |
(rhs.R_component_1() == lhs)&&
|
williamr@2
|
1135 |
(rhs.R_component_2() == static_cast<T>(0))&&
|
williamr@2
|
1136 |
(rhs.R_component_3() == static_cast<T>(0))&&
|
williamr@2
|
1137 |
(rhs.R_component_4() == static_cast<T>(0))
|
williamr@2
|
1138 |
);
|
williamr@2
|
1139 |
}
|
williamr@2
|
1140 |
|
williamr@2
|
1141 |
|
williamr@2
|
1142 |
template<typename T>
|
williamr@2
|
1143 |
inline bool operator == (quaternion<T> const & lhs, T const & rhs)
|
williamr@2
|
1144 |
{
|
williamr@2
|
1145 |
return (
|
williamr@2
|
1146 |
(lhs.R_component_1() == rhs)&&
|
williamr@2
|
1147 |
(lhs.R_component_2() == static_cast<T>(0))&&
|
williamr@2
|
1148 |
(lhs.R_component_3() == static_cast<T>(0))&&
|
williamr@2
|
1149 |
(lhs.R_component_4() == static_cast<T>(0))
|
williamr@2
|
1150 |
);
|
williamr@2
|
1151 |
}
|
williamr@2
|
1152 |
|
williamr@2
|
1153 |
|
williamr@2
|
1154 |
template<typename T>
|
williamr@2
|
1155 |
inline bool operator == (::std::complex<T> const & lhs, quaternion<T> const & rhs)
|
williamr@2
|
1156 |
{
|
williamr@2
|
1157 |
return (
|
williamr@2
|
1158 |
(rhs.R_component_1() == lhs.real())&&
|
williamr@2
|
1159 |
(rhs.R_component_2() == lhs.imag())&&
|
williamr@2
|
1160 |
(rhs.R_component_3() == static_cast<T>(0))&&
|
williamr@2
|
1161 |
(rhs.R_component_4() == static_cast<T>(0))
|
williamr@2
|
1162 |
);
|
williamr@2
|
1163 |
}
|
williamr@2
|
1164 |
|
williamr@2
|
1165 |
|
williamr@2
|
1166 |
template<typename T>
|
williamr@2
|
1167 |
inline bool operator == (quaternion<T> const & lhs, ::std::complex<T> const & rhs)
|
williamr@2
|
1168 |
{
|
williamr@2
|
1169 |
return (
|
williamr@2
|
1170 |
(lhs.R_component_1() == rhs.real())&&
|
williamr@2
|
1171 |
(lhs.R_component_2() == rhs.imag())&&
|
williamr@2
|
1172 |
(lhs.R_component_3() == static_cast<T>(0))&&
|
williamr@2
|
1173 |
(lhs.R_component_4() == static_cast<T>(0))
|
williamr@2
|
1174 |
);
|
williamr@2
|
1175 |
}
|
williamr@2
|
1176 |
|
williamr@2
|
1177 |
|
williamr@2
|
1178 |
template<typename T>
|
williamr@2
|
1179 |
inline bool operator == (quaternion<T> const & lhs, quaternion<T> const & rhs)
|
williamr@2
|
1180 |
{
|
williamr@2
|
1181 |
return (
|
williamr@2
|
1182 |
(rhs.R_component_1() == lhs.R_component_1())&&
|
williamr@2
|
1183 |
(rhs.R_component_2() == lhs.R_component_2())&&
|
williamr@2
|
1184 |
(rhs.R_component_3() == lhs.R_component_3())&&
|
williamr@2
|
1185 |
(rhs.R_component_4() == lhs.R_component_4())
|
williamr@2
|
1186 |
);
|
williamr@2
|
1187 |
}
|
williamr@2
|
1188 |
|
williamr@2
|
1189 |
|
williamr@2
|
1190 |
#define BOOST_QUATERNION_NOT_EQUAL_GENERATOR \
|
williamr@2
|
1191 |
{ \
|
williamr@2
|
1192 |
return(!(lhs == rhs)); \
|
williamr@2
|
1193 |
}
|
williamr@2
|
1194 |
|
williamr@2
|
1195 |
template<typename T>
|
williamr@2
|
1196 |
inline bool operator != (T const & lhs, quaternion<T> const & rhs)
|
williamr@2
|
1197 |
BOOST_QUATERNION_NOT_EQUAL_GENERATOR
|
williamr@2
|
1198 |
|
williamr@2
|
1199 |
template<typename T>
|
williamr@2
|
1200 |
inline bool operator != (quaternion<T> const & lhs, T const & rhs)
|
williamr@2
|
1201 |
BOOST_QUATERNION_NOT_EQUAL_GENERATOR
|
williamr@2
|
1202 |
|
williamr@2
|
1203 |
template<typename T>
|
williamr@2
|
1204 |
inline bool operator != (::std::complex<T> const & lhs, quaternion<T> const & rhs)
|
williamr@2
|
1205 |
BOOST_QUATERNION_NOT_EQUAL_GENERATOR
|
williamr@2
|
1206 |
|
williamr@2
|
1207 |
template<typename T>
|
williamr@2
|
1208 |
inline bool operator != (quaternion<T> const & lhs, ::std::complex<T> const & rhs)
|
williamr@2
|
1209 |
BOOST_QUATERNION_NOT_EQUAL_GENERATOR
|
williamr@2
|
1210 |
|
williamr@2
|
1211 |
template<typename T>
|
williamr@2
|
1212 |
inline bool operator != (quaternion<T> const & lhs, quaternion<T> const & rhs)
|
williamr@2
|
1213 |
BOOST_QUATERNION_NOT_EQUAL_GENERATOR
|
williamr@2
|
1214 |
|
williamr@2
|
1215 |
#undef BOOST_QUATERNION_NOT_EQUAL_GENERATOR
|
williamr@2
|
1216 |
|
williamr@2
|
1217 |
|
williamr@2
|
1218 |
// Note: we allow the following formats, whith a, b, c, and d reals
|
williamr@2
|
1219 |
// a
|
williamr@2
|
1220 |
// (a), (a,b), (a,b,c), (a,b,c,d)
|
williamr@2
|
1221 |
// (a,(c)), (a,(c,d)), ((a)), ((a),c), ((a),(c)), ((a),(c,d)), ((a,b)), ((a,b),c), ((a,b),(c)), ((a,b),(c,d))
|
williamr@2
|
1222 |
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
williamr@2
|
1223 |
template<typename T>
|
williamr@2
|
1224 |
std::istream & operator >> ( ::std::istream & is,
|
williamr@2
|
1225 |
quaternion<T> & q)
|
williamr@2
|
1226 |
#else
|
williamr@2
|
1227 |
template<typename T, typename charT, class traits>
|
williamr@2
|
1228 |
::std::basic_istream<charT,traits> & operator >> ( ::std::basic_istream<charT,traits> & is,
|
williamr@2
|
1229 |
quaternion<T> & q)
|
williamr@2
|
1230 |
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
williamr@2
|
1231 |
{
|
williamr@2
|
1232 |
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
williamr@2
|
1233 |
typedef char charT;
|
williamr@2
|
1234 |
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
williamr@2
|
1235 |
|
williamr@2
|
1236 |
#ifdef BOOST_NO_STD_LOCALE
|
williamr@2
|
1237 |
#else
|
williamr@2
|
1238 |
const ::std::ctype<charT> & ct = ::std::use_facet< ::std::ctype<charT> >(is.getloc());
|
williamr@2
|
1239 |
#endif /* BOOST_NO_STD_LOCALE */
|
williamr@2
|
1240 |
|
williamr@2
|
1241 |
T a = T();
|
williamr@2
|
1242 |
T b = T();
|
williamr@2
|
1243 |
T c = T();
|
williamr@2
|
1244 |
T d = T();
|
williamr@2
|
1245 |
|
williamr@2
|
1246 |
::std::complex<T> u = ::std::complex<T>();
|
williamr@2
|
1247 |
::std::complex<T> v = ::std::complex<T>();
|
williamr@2
|
1248 |
|
williamr@2
|
1249 |
charT ch = charT();
|
williamr@2
|
1250 |
char cc;
|
williamr@2
|
1251 |
|
williamr@2
|
1252 |
is >> ch; // get the first lexeme
|
williamr@2
|
1253 |
|
williamr@2
|
1254 |
if (!is.good()) goto finish;
|
williamr@2
|
1255 |
|
williamr@2
|
1256 |
#ifdef BOOST_NO_STD_LOCALE
|
williamr@2
|
1257 |
cc = ch;
|
williamr@2
|
1258 |
#else
|
williamr@2
|
1259 |
cc = ct.narrow(ch, char());
|
williamr@2
|
1260 |
#endif /* BOOST_NO_STD_LOCALE */
|
williamr@2
|
1261 |
|
williamr@2
|
1262 |
if (cc == '(') // read "(", possible: (a), (a,b), (a,b,c), (a,b,c,d), (a,(c)), (a,(c,d)), ((a)), ((a),c), ((a),(c)), ((a),(c,d)), ((a,b)), ((a,b),c), ((a,b),(c)), ((a,b,),(c,d,))
|
williamr@2
|
1263 |
{
|
williamr@2
|
1264 |
is >> ch; // get the second lexeme
|
williamr@2
|
1265 |
|
williamr@2
|
1266 |
if (!is.good()) goto finish;
|
williamr@2
|
1267 |
|
williamr@2
|
1268 |
#ifdef BOOST_NO_STD_LOCALE
|
williamr@2
|
1269 |
cc = ch;
|
williamr@2
|
1270 |
#else
|
williamr@2
|
1271 |
cc = ct.narrow(ch, char());
|
williamr@2
|
1272 |
#endif /* BOOST_NO_STD_LOCALE */
|
williamr@2
|
1273 |
|
williamr@2
|
1274 |
if (cc == '(') // read "((", possible: ((a)), ((a),c), ((a),(c)), ((a),(c,d)), ((a,b)), ((a,b),c), ((a,b),(c)), ((a,b,),(c,d,))
|
williamr@2
|
1275 |
{
|
williamr@2
|
1276 |
is.putback(ch);
|
williamr@2
|
1277 |
|
williamr@2
|
1278 |
is >> u; // we extract the first and second components
|
williamr@2
|
1279 |
a = u.real();
|
williamr@2
|
1280 |
b = u.imag();
|
williamr@2
|
1281 |
|
williamr@2
|
1282 |
if (!is.good()) goto finish;
|
williamr@2
|
1283 |
|
williamr@2
|
1284 |
is >> ch; // get the next lexeme
|
williamr@2
|
1285 |
|
williamr@2
|
1286 |
if (!is.good()) goto finish;
|
williamr@2
|
1287 |
|
williamr@2
|
1288 |
#ifdef BOOST_NO_STD_LOCALE
|
williamr@2
|
1289 |
cc = ch;
|
williamr@2
|
1290 |
#else
|
williamr@2
|
1291 |
cc = ct.narrow(ch, char());
|
williamr@2
|
1292 |
#endif /* BOOST_NO_STD_LOCALE */
|
williamr@2
|
1293 |
|
williamr@2
|
1294 |
if (cc == ')') // format: ((a)) or ((a,b))
|
williamr@2
|
1295 |
{
|
williamr@2
|
1296 |
q = quaternion<T>(a,b);
|
williamr@2
|
1297 |
}
|
williamr@2
|
1298 |
else if (cc == ',') // read "((a)," or "((a,b),", possible: ((a),c), ((a),(c)), ((a),(c,d)), ((a,b),c), ((a,b),(c)), ((a,b,),(c,d,))
|
williamr@2
|
1299 |
{
|
williamr@2
|
1300 |
is >> v; // we extract the third and fourth components
|
williamr@2
|
1301 |
c = v.real();
|
williamr@2
|
1302 |
d = v.imag();
|
williamr@2
|
1303 |
|
williamr@2
|
1304 |
if (!is.good()) goto finish;
|
williamr@2
|
1305 |
|
williamr@2
|
1306 |
is >> ch; // get the last lexeme
|
williamr@2
|
1307 |
|
williamr@2
|
1308 |
if (!is.good()) goto finish;
|
williamr@2
|
1309 |
|
williamr@2
|
1310 |
#ifdef BOOST_NO_STD_LOCALE
|
williamr@2
|
1311 |
cc = ch;
|
williamr@2
|
1312 |
#else
|
williamr@2
|
1313 |
cc = ct.narrow(ch, char());
|
williamr@2
|
1314 |
#endif /* BOOST_NO_STD_LOCALE */
|
williamr@2
|
1315 |
|
williamr@2
|
1316 |
if (cc == ')') // format: ((a),c), ((a),(c)), ((a),(c,d)), ((a,b),c), ((a,b),(c)) or ((a,b,),(c,d,))
|
williamr@2
|
1317 |
{
|
williamr@2
|
1318 |
q = quaternion<T>(a,b,c,d);
|
williamr@2
|
1319 |
}
|
williamr@2
|
1320 |
else // error
|
williamr@2
|
1321 |
{
|
williamr@2
|
1322 |
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
williamr@2
|
1323 |
is.setstate(::std::ios::failbit);
|
williamr@2
|
1324 |
#else
|
williamr@2
|
1325 |
is.setstate(::std::ios_base::failbit);
|
williamr@2
|
1326 |
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
williamr@2
|
1327 |
}
|
williamr@2
|
1328 |
}
|
williamr@2
|
1329 |
else // error
|
williamr@2
|
1330 |
{
|
williamr@2
|
1331 |
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
williamr@2
|
1332 |
is.setstate(::std::ios::failbit);
|
williamr@2
|
1333 |
#else
|
williamr@2
|
1334 |
is.setstate(::std::ios_base::failbit);
|
williamr@2
|
1335 |
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
williamr@2
|
1336 |
}
|
williamr@2
|
1337 |
}
|
williamr@2
|
1338 |
else // read "(a", possible: (a), (a,b), (a,b,c), (a,b,c,d), (a,(c)), (a,(c,d))
|
williamr@2
|
1339 |
{
|
williamr@2
|
1340 |
is.putback(ch);
|
williamr@2
|
1341 |
|
williamr@2
|
1342 |
is >> a; // we extract the first component
|
williamr@2
|
1343 |
|
williamr@2
|
1344 |
if (!is.good()) goto finish;
|
williamr@2
|
1345 |
|
williamr@2
|
1346 |
is >> ch; // get the third lexeme
|
williamr@2
|
1347 |
|
williamr@2
|
1348 |
if (!is.good()) goto finish;
|
williamr@2
|
1349 |
|
williamr@2
|
1350 |
#ifdef BOOST_NO_STD_LOCALE
|
williamr@2
|
1351 |
cc = ch;
|
williamr@2
|
1352 |
#else
|
williamr@2
|
1353 |
cc = ct.narrow(ch, char());
|
williamr@2
|
1354 |
#endif /* BOOST_NO_STD_LOCALE */
|
williamr@2
|
1355 |
|
williamr@2
|
1356 |
if (cc == ')') // format: (a)
|
williamr@2
|
1357 |
{
|
williamr@2
|
1358 |
q = quaternion<T>(a);
|
williamr@2
|
1359 |
}
|
williamr@2
|
1360 |
else if (cc == ',') // read "(a,", possible: (a,b), (a,b,c), (a,b,c,d), (a,(c)), (a,(c,d))
|
williamr@2
|
1361 |
{
|
williamr@2
|
1362 |
is >> ch; // get the fourth lexeme
|
williamr@2
|
1363 |
|
williamr@2
|
1364 |
if (!is.good()) goto finish;
|
williamr@2
|
1365 |
|
williamr@2
|
1366 |
#ifdef BOOST_NO_STD_LOCALE
|
williamr@2
|
1367 |
cc = ch;
|
williamr@2
|
1368 |
#else
|
williamr@2
|
1369 |
cc = ct.narrow(ch, char());
|
williamr@2
|
1370 |
#endif /* BOOST_NO_STD_LOCALE */
|
williamr@2
|
1371 |
|
williamr@2
|
1372 |
if (cc == '(') // read "(a,(", possible: (a,(c)), (a,(c,d))
|
williamr@2
|
1373 |
{
|
williamr@2
|
1374 |
is.putback(ch);
|
williamr@2
|
1375 |
|
williamr@2
|
1376 |
is >> v; // we extract the third and fourth component
|
williamr@2
|
1377 |
|
williamr@2
|
1378 |
c = v.real();
|
williamr@2
|
1379 |
d = v.imag();
|
williamr@2
|
1380 |
|
williamr@2
|
1381 |
if (!is.good()) goto finish;
|
williamr@2
|
1382 |
|
williamr@2
|
1383 |
is >> ch; // get the ninth lexeme
|
williamr@2
|
1384 |
|
williamr@2
|
1385 |
if (!is.good()) goto finish;
|
williamr@2
|
1386 |
|
williamr@2
|
1387 |
#ifdef BOOST_NO_STD_LOCALE
|
williamr@2
|
1388 |
cc = ch;
|
williamr@2
|
1389 |
#else
|
williamr@2
|
1390 |
cc = ct.narrow(ch, char());
|
williamr@2
|
1391 |
#endif /* BOOST_NO_STD_LOCALE */
|
williamr@2
|
1392 |
|
williamr@2
|
1393 |
if (cc == ')') // format: (a,(c)) or (a,(c,d))
|
williamr@2
|
1394 |
{
|
williamr@2
|
1395 |
q = quaternion<T>(a,b,c,d);
|
williamr@2
|
1396 |
}
|
williamr@2
|
1397 |
else // error
|
williamr@2
|
1398 |
{
|
williamr@2
|
1399 |
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
williamr@2
|
1400 |
is.setstate(::std::ios::failbit);
|
williamr@2
|
1401 |
#else
|
williamr@2
|
1402 |
is.setstate(::std::ios_base::failbit);
|
williamr@2
|
1403 |
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
williamr@2
|
1404 |
}
|
williamr@2
|
1405 |
}
|
williamr@2
|
1406 |
else // read "(a,b", possible: (a,b), (a,b,c), (a,b,c,d)
|
williamr@2
|
1407 |
{
|
williamr@2
|
1408 |
is.putback(ch);
|
williamr@2
|
1409 |
|
williamr@2
|
1410 |
is >> b; // we extract the second component
|
williamr@2
|
1411 |
|
williamr@2
|
1412 |
if (!is.good()) goto finish;
|
williamr@2
|
1413 |
|
williamr@2
|
1414 |
is >> ch; // get the fifth lexeme
|
williamr@2
|
1415 |
|
williamr@2
|
1416 |
if (!is.good()) goto finish;
|
williamr@2
|
1417 |
|
williamr@2
|
1418 |
#ifdef BOOST_NO_STD_LOCALE
|
williamr@2
|
1419 |
cc = ch;
|
williamr@2
|
1420 |
#else
|
williamr@2
|
1421 |
cc = ct.narrow(ch, char());
|
williamr@2
|
1422 |
#endif /* BOOST_NO_STD_LOCALE */
|
williamr@2
|
1423 |
|
williamr@2
|
1424 |
if (cc == ')') // format: (a,b)
|
williamr@2
|
1425 |
{
|
williamr@2
|
1426 |
q = quaternion<T>(a,b);
|
williamr@2
|
1427 |
}
|
williamr@2
|
1428 |
else if (cc == ',') // read "(a,b,", possible: (a,b,c), (a,b,c,d)
|
williamr@2
|
1429 |
{
|
williamr@2
|
1430 |
is >> c; // we extract the third component
|
williamr@2
|
1431 |
|
williamr@2
|
1432 |
if (!is.good()) goto finish;
|
williamr@2
|
1433 |
|
williamr@2
|
1434 |
is >> ch; // get the seventh lexeme
|
williamr@2
|
1435 |
|
williamr@2
|
1436 |
if (!is.good()) goto finish;
|
williamr@2
|
1437 |
|
williamr@2
|
1438 |
#ifdef BOOST_NO_STD_LOCALE
|
williamr@2
|
1439 |
cc = ch;
|
williamr@2
|
1440 |
#else
|
williamr@2
|
1441 |
cc = ct.narrow(ch, char());
|
williamr@2
|
1442 |
#endif /* BOOST_NO_STD_LOCALE */
|
williamr@2
|
1443 |
|
williamr@2
|
1444 |
if (cc == ')') // format: (a,b,c)
|
williamr@2
|
1445 |
{
|
williamr@2
|
1446 |
q = quaternion<T>(a,b,c);
|
williamr@2
|
1447 |
}
|
williamr@2
|
1448 |
else if (cc == ',') // read "(a,b,c,", possible: (a,b,c,d)
|
williamr@2
|
1449 |
{
|
williamr@2
|
1450 |
is >> d; // we extract the fourth component
|
williamr@2
|
1451 |
|
williamr@2
|
1452 |
if (!is.good()) goto finish;
|
williamr@2
|
1453 |
|
williamr@2
|
1454 |
is >> ch; // get the ninth lexeme
|
williamr@2
|
1455 |
|
williamr@2
|
1456 |
if (!is.good()) goto finish;
|
williamr@2
|
1457 |
|
williamr@2
|
1458 |
#ifdef BOOST_NO_STD_LOCALE
|
williamr@2
|
1459 |
cc = ch;
|
williamr@2
|
1460 |
#else
|
williamr@2
|
1461 |
cc = ct.narrow(ch, char());
|
williamr@2
|
1462 |
#endif /* BOOST_NO_STD_LOCALE */
|
williamr@2
|
1463 |
|
williamr@2
|
1464 |
if (cc == ')') // format: (a,b,c,d)
|
williamr@2
|
1465 |
{
|
williamr@2
|
1466 |
q = quaternion<T>(a,b,c,d);
|
williamr@2
|
1467 |
}
|
williamr@2
|
1468 |
else // error
|
williamr@2
|
1469 |
{
|
williamr@2
|
1470 |
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
williamr@2
|
1471 |
is.setstate(::std::ios::failbit);
|
williamr@2
|
1472 |
#else
|
williamr@2
|
1473 |
is.setstate(::std::ios_base::failbit);
|
williamr@2
|
1474 |
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
williamr@2
|
1475 |
}
|
williamr@2
|
1476 |
}
|
williamr@2
|
1477 |
else // error
|
williamr@2
|
1478 |
{
|
williamr@2
|
1479 |
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
williamr@2
|
1480 |
is.setstate(::std::ios::failbit);
|
williamr@2
|
1481 |
#else
|
williamr@2
|
1482 |
is.setstate(::std::ios_base::failbit);
|
williamr@2
|
1483 |
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
williamr@2
|
1484 |
}
|
williamr@2
|
1485 |
}
|
williamr@2
|
1486 |
else // error
|
williamr@2
|
1487 |
{
|
williamr@2
|
1488 |
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
williamr@2
|
1489 |
is.setstate(::std::ios::failbit);
|
williamr@2
|
1490 |
#else
|
williamr@2
|
1491 |
is.setstate(::std::ios_base::failbit);
|
williamr@2
|
1492 |
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
williamr@2
|
1493 |
}
|
williamr@2
|
1494 |
}
|
williamr@2
|
1495 |
}
|
williamr@2
|
1496 |
else // error
|
williamr@2
|
1497 |
{
|
williamr@2
|
1498 |
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
williamr@2
|
1499 |
is.setstate(::std::ios::failbit);
|
williamr@2
|
1500 |
#else
|
williamr@2
|
1501 |
is.setstate(::std::ios_base::failbit);
|
williamr@2
|
1502 |
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
williamr@2
|
1503 |
}
|
williamr@2
|
1504 |
}
|
williamr@2
|
1505 |
}
|
williamr@2
|
1506 |
else // format: a
|
williamr@2
|
1507 |
{
|
williamr@2
|
1508 |
is.putback(ch);
|
williamr@2
|
1509 |
|
williamr@2
|
1510 |
is >> a; // we extract the first component
|
williamr@2
|
1511 |
|
williamr@2
|
1512 |
if (!is.good()) goto finish;
|
williamr@2
|
1513 |
|
williamr@2
|
1514 |
q = quaternion<T>(a);
|
williamr@2
|
1515 |
}
|
williamr@2
|
1516 |
|
williamr@2
|
1517 |
finish:
|
williamr@2
|
1518 |
return(is);
|
williamr@2
|
1519 |
}
|
williamr@2
|
1520 |
|
williamr@2
|
1521 |
|
williamr@2
|
1522 |
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
williamr@2
|
1523 |
template<typename T>
|
williamr@2
|
1524 |
::std::ostream & operator << ( ::std::ostream & os,
|
williamr@2
|
1525 |
quaternion<T> const & q)
|
williamr@2
|
1526 |
#else
|
williamr@2
|
1527 |
template<typename T, typename charT, class traits>
|
williamr@2
|
1528 |
::std::basic_ostream<charT,traits> & operator << ( ::std::basic_ostream<charT,traits> & os,
|
williamr@2
|
1529 |
quaternion<T> const & q)
|
williamr@2
|
1530 |
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
williamr@2
|
1531 |
{
|
williamr@2
|
1532 |
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
williamr@2
|
1533 |
::std::ostringstream s;
|
williamr@2
|
1534 |
#else
|
williamr@2
|
1535 |
::std::basic_ostringstream<charT,traits> s;
|
williamr@2
|
1536 |
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
williamr@2
|
1537 |
|
williamr@2
|
1538 |
s.flags(os.flags());
|
williamr@2
|
1539 |
#ifdef BOOST_NO_STD_LOCALE
|
williamr@2
|
1540 |
#else
|
williamr@2
|
1541 |
s.imbue(os.getloc());
|
williamr@2
|
1542 |
#endif /* BOOST_NO_STD_LOCALE */
|
williamr@2
|
1543 |
s.precision(os.precision());
|
williamr@2
|
1544 |
|
williamr@2
|
1545 |
s << '(' << q.R_component_1() << ','
|
williamr@2
|
1546 |
<< q.R_component_2() << ','
|
williamr@2
|
1547 |
<< q.R_component_3() << ','
|
williamr@2
|
1548 |
<< q.R_component_4() << ')';
|
williamr@2
|
1549 |
|
williamr@2
|
1550 |
return os << s.str();
|
williamr@2
|
1551 |
}
|
williamr@2
|
1552 |
|
williamr@2
|
1553 |
|
williamr@2
|
1554 |
// values
|
williamr@2
|
1555 |
|
williamr@2
|
1556 |
template<typename T>
|
williamr@2
|
1557 |
inline T real(quaternion<T> const & q)
|
williamr@2
|
1558 |
{
|
williamr@2
|
1559 |
return(q.real());
|
williamr@2
|
1560 |
}
|
williamr@2
|
1561 |
|
williamr@2
|
1562 |
|
williamr@2
|
1563 |
template<typename T>
|
williamr@2
|
1564 |
inline quaternion<T> unreal(quaternion<T> const & q)
|
williamr@2
|
1565 |
{
|
williamr@2
|
1566 |
return(q.unreal());
|
williamr@2
|
1567 |
}
|
williamr@2
|
1568 |
|
williamr@2
|
1569 |
|
williamr@2
|
1570 |
#define BOOST_QUATERNION_VALARRAY_LOADER \
|
williamr@2
|
1571 |
using ::std::valarray; \
|
williamr@2
|
1572 |
\
|
williamr@2
|
1573 |
valarray<T> temp(4); \
|
williamr@2
|
1574 |
\
|
williamr@2
|
1575 |
temp[0] = q.R_component_1(); \
|
williamr@2
|
1576 |
temp[1] = q.R_component_2(); \
|
williamr@2
|
1577 |
temp[2] = q.R_component_3(); \
|
williamr@2
|
1578 |
temp[3] = q.R_component_4();
|
williamr@2
|
1579 |
|
williamr@2
|
1580 |
|
williamr@2
|
1581 |
template<typename T>
|
williamr@2
|
1582 |
inline T sup(quaternion<T> const & q)
|
williamr@2
|
1583 |
{
|
williamr@2
|
1584 |
#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
|
williamr@2
|
1585 |
using ::std::abs;
|
williamr@2
|
1586 |
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
williamr@2
|
1587 |
|
williamr@2
|
1588 |
BOOST_QUATERNION_VALARRAY_LOADER
|
williamr@2
|
1589 |
|
williamr@2
|
1590 |
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
williamr@2
|
1591 |
return((BOOST_GET_VALARRAY(T, abs(temp)).max)());
|
williamr@2
|
1592 |
#else
|
williamr@2
|
1593 |
return((abs(temp).max)());
|
williamr@2
|
1594 |
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
williamr@2
|
1595 |
}
|
williamr@2
|
1596 |
|
williamr@2
|
1597 |
|
williamr@2
|
1598 |
template<typename T>
|
williamr@2
|
1599 |
inline T l1(quaternion<T> const & q)
|
williamr@2
|
1600 |
{
|
williamr@2
|
1601 |
#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
|
williamr@2
|
1602 |
using ::std::abs;
|
williamr@2
|
1603 |
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
williamr@2
|
1604 |
|
williamr@2
|
1605 |
BOOST_QUATERNION_VALARRAY_LOADER
|
williamr@2
|
1606 |
|
williamr@2
|
1607 |
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
williamr@2
|
1608 |
return(BOOST_GET_VALARRAY(T, abs(temp)).sum());
|
williamr@2
|
1609 |
#else
|
williamr@2
|
1610 |
return(abs(temp).sum());
|
williamr@2
|
1611 |
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
williamr@2
|
1612 |
}
|
williamr@2
|
1613 |
|
williamr@2
|
1614 |
|
williamr@2
|
1615 |
template<typename T>
|
williamr@2
|
1616 |
inline T abs(quaternion<T> const & q)
|
williamr@2
|
1617 |
{
|
williamr@2
|
1618 |
#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
|
williamr@2
|
1619 |
using ::std::abs;
|
williamr@2
|
1620 |
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
williamr@2
|
1621 |
|
williamr@2
|
1622 |
using ::std::sqrt;
|
williamr@2
|
1623 |
|
williamr@2
|
1624 |
BOOST_QUATERNION_VALARRAY_LOADER
|
williamr@2
|
1625 |
|
williamr@2
|
1626 |
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
williamr@2
|
1627 |
T maxim = (BOOST_GET_VALARRAY(T, abs(temp)).max)(); // overflow protection
|
williamr@2
|
1628 |
#else
|
williamr@2
|
1629 |
T maxim = (abs(temp).max)(); // overflow protection
|
williamr@2
|
1630 |
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
williamr@2
|
1631 |
|
williamr@2
|
1632 |
if (maxim == static_cast<T>(0))
|
williamr@2
|
1633 |
{
|
williamr@2
|
1634 |
return(maxim);
|
williamr@2
|
1635 |
}
|
williamr@2
|
1636 |
else
|
williamr@2
|
1637 |
{
|
williamr@2
|
1638 |
T mixam = static_cast<T>(1)/maxim; // prefer multiplications over divisions
|
williamr@2
|
1639 |
|
williamr@2
|
1640 |
temp *= mixam;
|
williamr@2
|
1641 |
|
williamr@2
|
1642 |
temp *= temp;
|
williamr@2
|
1643 |
|
williamr@2
|
1644 |
return(maxim*sqrt(temp.sum()));
|
williamr@2
|
1645 |
}
|
williamr@2
|
1646 |
|
williamr@2
|
1647 |
//return(sqrt(norm(q)));
|
williamr@2
|
1648 |
}
|
williamr@2
|
1649 |
|
williamr@2
|
1650 |
|
williamr@2
|
1651 |
#undef BOOST_QUATERNION_VALARRAY_LOADER
|
williamr@2
|
1652 |
|
williamr@2
|
1653 |
|
williamr@2
|
1654 |
// Note: This is the Cayley norm, not the Euclidian norm...
|
williamr@2
|
1655 |
|
williamr@2
|
1656 |
template<typename T>
|
williamr@2
|
1657 |
inline T norm(quaternion<T>const & q)
|
williamr@2
|
1658 |
{
|
williamr@2
|
1659 |
return(real(q*conj(q)));
|
williamr@2
|
1660 |
}
|
williamr@2
|
1661 |
|
williamr@2
|
1662 |
|
williamr@2
|
1663 |
template<typename T>
|
williamr@2
|
1664 |
inline quaternion<T> conj(quaternion<T> const & q)
|
williamr@2
|
1665 |
{
|
williamr@2
|
1666 |
return(quaternion<T>( +q.R_component_1(),
|
williamr@2
|
1667 |
-q.R_component_2(),
|
williamr@2
|
1668 |
-q.R_component_3(),
|
williamr@2
|
1669 |
-q.R_component_4()));
|
williamr@2
|
1670 |
}
|
williamr@2
|
1671 |
|
williamr@2
|
1672 |
|
williamr@2
|
1673 |
template<typename T>
|
williamr@2
|
1674 |
inline quaternion<T> spherical( T const & rho,
|
williamr@2
|
1675 |
T const & theta,
|
williamr@2
|
1676 |
T const & phi1,
|
williamr@2
|
1677 |
T const & phi2)
|
williamr@2
|
1678 |
{
|
williamr@2
|
1679 |
using ::std::cos;
|
williamr@2
|
1680 |
using ::std::sin;
|
williamr@2
|
1681 |
|
williamr@2
|
1682 |
//T a = cos(theta)*cos(phi1)*cos(phi2);
|
williamr@2
|
1683 |
//T b = sin(theta)*cos(phi1)*cos(phi2);
|
williamr@2
|
1684 |
//T c = sin(phi1)*cos(phi2);
|
williamr@2
|
1685 |
//T d = sin(phi2);
|
williamr@2
|
1686 |
|
williamr@2
|
1687 |
T courrant = static_cast<T>(1);
|
williamr@2
|
1688 |
|
williamr@2
|
1689 |
T d = sin(phi2);
|
williamr@2
|
1690 |
|
williamr@2
|
1691 |
courrant *= cos(phi2);
|
williamr@2
|
1692 |
|
williamr@2
|
1693 |
T c = sin(phi1)*courrant;
|
williamr@2
|
1694 |
|
williamr@2
|
1695 |
courrant *= cos(phi1);
|
williamr@2
|
1696 |
|
williamr@2
|
1697 |
T b = sin(theta)*courrant;
|
williamr@2
|
1698 |
T a = cos(theta)*courrant;
|
williamr@2
|
1699 |
|
williamr@2
|
1700 |
return(rho*quaternion<T>(a,b,c,d));
|
williamr@2
|
1701 |
}
|
williamr@2
|
1702 |
|
williamr@2
|
1703 |
|
williamr@2
|
1704 |
template<typename T>
|
williamr@2
|
1705 |
inline quaternion<T> semipolar( T const & rho,
|
williamr@2
|
1706 |
T const & alpha,
|
williamr@2
|
1707 |
T const & theta1,
|
williamr@2
|
1708 |
T const & theta2)
|
williamr@2
|
1709 |
{
|
williamr@2
|
1710 |
using ::std::cos;
|
williamr@2
|
1711 |
using ::std::sin;
|
williamr@2
|
1712 |
|
williamr@2
|
1713 |
T a = cos(alpha)*cos(theta1);
|
williamr@2
|
1714 |
T b = cos(alpha)*sin(theta1);
|
williamr@2
|
1715 |
T c = sin(alpha)*cos(theta2);
|
williamr@2
|
1716 |
T d = sin(alpha)*sin(theta2);
|
williamr@2
|
1717 |
|
williamr@2
|
1718 |
return(rho*quaternion<T>(a,b,c,d));
|
williamr@2
|
1719 |
}
|
williamr@2
|
1720 |
|
williamr@2
|
1721 |
|
williamr@2
|
1722 |
template<typename T>
|
williamr@2
|
1723 |
inline quaternion<T> multipolar( T const & rho1,
|
williamr@2
|
1724 |
T const & theta1,
|
williamr@2
|
1725 |
T const & rho2,
|
williamr@2
|
1726 |
T const & theta2)
|
williamr@2
|
1727 |
{
|
williamr@2
|
1728 |
using ::std::cos;
|
williamr@2
|
1729 |
using ::std::sin;
|
williamr@2
|
1730 |
|
williamr@2
|
1731 |
T a = rho1*cos(theta1);
|
williamr@2
|
1732 |
T b = rho1*sin(theta1);
|
williamr@2
|
1733 |
T c = rho2*cos(theta2);
|
williamr@2
|
1734 |
T d = rho2*sin(theta2);
|
williamr@2
|
1735 |
|
williamr@2
|
1736 |
return(quaternion<T>(a,b,c,d));
|
williamr@2
|
1737 |
}
|
williamr@2
|
1738 |
|
williamr@2
|
1739 |
|
williamr@2
|
1740 |
template<typename T>
|
williamr@2
|
1741 |
inline quaternion<T> cylindrospherical( T const & t,
|
williamr@2
|
1742 |
T const & radius,
|
williamr@2
|
1743 |
T const & longitude,
|
williamr@2
|
1744 |
T const & latitude)
|
williamr@2
|
1745 |
{
|
williamr@2
|
1746 |
using ::std::cos;
|
williamr@2
|
1747 |
using ::std::sin;
|
williamr@2
|
1748 |
|
williamr@2
|
1749 |
|
williamr@2
|
1750 |
|
williamr@2
|
1751 |
T b = radius*cos(longitude)*cos(latitude);
|
williamr@2
|
1752 |
T c = radius*sin(longitude)*cos(latitude);
|
williamr@2
|
1753 |
T d = radius*sin(latitude);
|
williamr@2
|
1754 |
|
williamr@2
|
1755 |
return(quaternion<T>(t,b,c,d));
|
williamr@2
|
1756 |
}
|
williamr@2
|
1757 |
|
williamr@2
|
1758 |
|
williamr@2
|
1759 |
template<typename T>
|
williamr@2
|
1760 |
inline quaternion<T> cylindrical(T const & r,
|
williamr@2
|
1761 |
T const & angle,
|
williamr@2
|
1762 |
T const & h1,
|
williamr@2
|
1763 |
T const & h2)
|
williamr@2
|
1764 |
{
|
williamr@2
|
1765 |
using ::std::cos;
|
williamr@2
|
1766 |
using ::std::sin;
|
williamr@2
|
1767 |
|
williamr@2
|
1768 |
T a = r*cos(angle);
|
williamr@2
|
1769 |
T b = r*sin(angle);
|
williamr@2
|
1770 |
|
williamr@2
|
1771 |
return(quaternion<T>(a,b,h1,h2));
|
williamr@2
|
1772 |
}
|
williamr@2
|
1773 |
|
williamr@2
|
1774 |
|
williamr@2
|
1775 |
// transcendentals
|
williamr@2
|
1776 |
// (please see the documentation)
|
williamr@2
|
1777 |
|
williamr@2
|
1778 |
|
williamr@2
|
1779 |
template<typename T>
|
williamr@2
|
1780 |
inline quaternion<T> exp(quaternion<T> const & q)
|
williamr@2
|
1781 |
{
|
williamr@2
|
1782 |
using ::std::exp;
|
williamr@2
|
1783 |
using ::std::cos;
|
williamr@2
|
1784 |
|
williamr@2
|
1785 |
using ::boost::math::sinc_pi;
|
williamr@2
|
1786 |
|
williamr@2
|
1787 |
T u = exp(real(q));
|
williamr@2
|
1788 |
|
williamr@2
|
1789 |
T z = abs(unreal(q));
|
williamr@2
|
1790 |
|
williamr@2
|
1791 |
T w = sinc_pi(z);
|
williamr@2
|
1792 |
|
williamr@2
|
1793 |
return(u*quaternion<T>(cos(z),
|
williamr@2
|
1794 |
w*q.R_component_2(), w*q.R_component_3(),
|
williamr@2
|
1795 |
w*q.R_component_4()));
|
williamr@2
|
1796 |
}
|
williamr@2
|
1797 |
|
williamr@2
|
1798 |
|
williamr@2
|
1799 |
template<typename T>
|
williamr@2
|
1800 |
inline quaternion<T> cos(quaternion<T> const & q)
|
williamr@2
|
1801 |
{
|
williamr@2
|
1802 |
using ::std::sin;
|
williamr@2
|
1803 |
using ::std::cos;
|
williamr@2
|
1804 |
using ::std::cosh;
|
williamr@2
|
1805 |
|
williamr@2
|
1806 |
using ::boost::math::sinhc_pi;
|
williamr@2
|
1807 |
|
williamr@2
|
1808 |
T z = abs(unreal(q));
|
williamr@2
|
1809 |
|
williamr@2
|
1810 |
T w = -sin(q.real())*sinhc_pi(z);
|
williamr@2
|
1811 |
|
williamr@2
|
1812 |
return(quaternion<T>(cos(q.real())*cosh(z),
|
williamr@2
|
1813 |
w*q.R_component_2(), w*q.R_component_3(),
|
williamr@2
|
1814 |
w*q.R_component_4()));
|
williamr@2
|
1815 |
}
|
williamr@2
|
1816 |
|
williamr@2
|
1817 |
|
williamr@2
|
1818 |
template<typename T>
|
williamr@2
|
1819 |
inline quaternion<T> sin(quaternion<T> const & q)
|
williamr@2
|
1820 |
{
|
williamr@2
|
1821 |
using ::std::sin;
|
williamr@2
|
1822 |
using ::std::cos;
|
williamr@2
|
1823 |
using ::std::cosh;
|
williamr@2
|
1824 |
|
williamr@2
|
1825 |
using ::boost::math::sinhc_pi;
|
williamr@2
|
1826 |
|
williamr@2
|
1827 |
T z = abs(unreal(q));
|
williamr@2
|
1828 |
|
williamr@2
|
1829 |
T w = +cos(q.real())*sinhc_pi(z);
|
williamr@2
|
1830 |
|
williamr@2
|
1831 |
return(quaternion<T>(sin(q.real())*cosh(z),
|
williamr@2
|
1832 |
w*q.R_component_2(), w*q.R_component_3(),
|
williamr@2
|
1833 |
w*q.R_component_4()));
|
williamr@2
|
1834 |
}
|
williamr@2
|
1835 |
|
williamr@2
|
1836 |
|
williamr@2
|
1837 |
template<typename T>
|
williamr@2
|
1838 |
inline quaternion<T> tan(quaternion<T> const & q)
|
williamr@2
|
1839 |
{
|
williamr@2
|
1840 |
return(sin(q)/cos(q));
|
williamr@2
|
1841 |
}
|
williamr@2
|
1842 |
|
williamr@2
|
1843 |
|
williamr@2
|
1844 |
template<typename T>
|
williamr@2
|
1845 |
inline quaternion<T> cosh(quaternion<T> const & q)
|
williamr@2
|
1846 |
{
|
williamr@2
|
1847 |
return((exp(+q)+exp(-q))/static_cast<T>(2));
|
williamr@2
|
1848 |
}
|
williamr@2
|
1849 |
|
williamr@2
|
1850 |
|
williamr@2
|
1851 |
template<typename T>
|
williamr@2
|
1852 |
inline quaternion<T> sinh(quaternion<T> const & q)
|
williamr@2
|
1853 |
{
|
williamr@2
|
1854 |
return((exp(+q)-exp(-q))/static_cast<T>(2));
|
williamr@2
|
1855 |
}
|
williamr@2
|
1856 |
|
williamr@2
|
1857 |
|
williamr@2
|
1858 |
template<typename T>
|
williamr@2
|
1859 |
inline quaternion<T> tanh(quaternion<T> const & q)
|
williamr@2
|
1860 |
{
|
williamr@2
|
1861 |
return(sinh(q)/cosh(q));
|
williamr@2
|
1862 |
}
|
williamr@2
|
1863 |
|
williamr@2
|
1864 |
|
williamr@2
|
1865 |
template<typename T>
|
williamr@2
|
1866 |
quaternion<T> pow(quaternion<T> const & q,
|
williamr@2
|
1867 |
int n)
|
williamr@2
|
1868 |
{
|
williamr@2
|
1869 |
if (n > 1)
|
williamr@2
|
1870 |
{
|
williamr@2
|
1871 |
int m = n>>1;
|
williamr@2
|
1872 |
|
williamr@2
|
1873 |
quaternion<T> result = pow(q, m);
|
williamr@2
|
1874 |
|
williamr@2
|
1875 |
result *= result;
|
williamr@2
|
1876 |
|
williamr@2
|
1877 |
if (n != (m<<1))
|
williamr@2
|
1878 |
{
|
williamr@2
|
1879 |
result *= q; // n odd
|
williamr@2
|
1880 |
}
|
williamr@2
|
1881 |
|
williamr@2
|
1882 |
return(result);
|
williamr@2
|
1883 |
}
|
williamr@2
|
1884 |
else if (n == 1)
|
williamr@2
|
1885 |
{
|
williamr@2
|
1886 |
return(q);
|
williamr@2
|
1887 |
}
|
williamr@2
|
1888 |
else if (n == 0)
|
williamr@2
|
1889 |
{
|
williamr@2
|
1890 |
return(quaternion<T>(1));
|
williamr@2
|
1891 |
}
|
williamr@2
|
1892 |
else /* n < 0 */
|
williamr@2
|
1893 |
{
|
williamr@2
|
1894 |
return(pow(quaternion<T>(1)/q,-n));
|
williamr@2
|
1895 |
}
|
williamr@2
|
1896 |
}
|
williamr@2
|
1897 |
|
williamr@2
|
1898 |
|
williamr@2
|
1899 |
// helper templates for converting copy constructors (definition)
|
williamr@2
|
1900 |
|
williamr@2
|
1901 |
namespace detail
|
williamr@2
|
1902 |
{
|
williamr@2
|
1903 |
|
williamr@2
|
1904 |
template< typename T,
|
williamr@2
|
1905 |
typename U
|
williamr@2
|
1906 |
>
|
williamr@2
|
1907 |
quaternion<T> quaternion_type_converter(quaternion<U> const & rhs)
|
williamr@2
|
1908 |
{
|
williamr@2
|
1909 |
return(quaternion<T>( static_cast<T>(rhs.R_component_1()),
|
williamr@2
|
1910 |
static_cast<T>(rhs.R_component_2()),
|
williamr@2
|
1911 |
static_cast<T>(rhs.R_component_3()),
|
williamr@2
|
1912 |
static_cast<T>(rhs.R_component_4())));
|
williamr@2
|
1913 |
}
|
williamr@2
|
1914 |
}
|
williamr@2
|
1915 |
}
|
williamr@2
|
1916 |
}
|
williamr@2
|
1917 |
|
williamr@2
|
1918 |
|
williamr@2
|
1919 |
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
williamr@2
|
1920 |
#undef BOOST_GET_VALARRAY
|
williamr@2
|
1921 |
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
williamr@2
|
1922 |
|
williamr@2
|
1923 |
|
williamr@2
|
1924 |
#endif /* BOOST_QUATERNION_HPP */
|