boost/multiprecision/number.hpp
/////////////////////////////////////////////////////////////////////////////// // Copyright 2011 John Maddock. Distributed under the Boost // Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) #ifndef BOOST_MATH_EXTENDED_REAL_HPP #define BOOST_MATH_EXTENDED_REAL_HPP #include <boost/cstdint.hpp> #include <boost/mpl/max.hpp> #include <boost/mpl/plus.hpp> #include <boost/mpl/or.hpp> #include <boost/mpl/find_if.hpp> #include <boost/assert.hpp> #include <boost/type_traits/remove_pointer.hpp> #include <boost/type_traits/is_signed.hpp> #include <boost/type_traits/is_unsigned.hpp> #include <boost/type_traits/is_floating_point.hpp> #include <boost/type_traits/is_integral.hpp> #include <boost/type_traits/make_unsigned.hpp> #include <boost/throw_exception.hpp> #include <boost/multiprecision/detail/generic_interconvert.hpp> #include <boost/multiprecision/detail/number_compare.hpp> #include <boost/multiprecision/traits/is_restricted_conversion.hpp> #include <istream> // stream operators #include <cstdio> // EOF #include <cctype> // isspace namespace boost{ namespace multiprecision{ #ifdef BOOST_MSVC // warning C4127: conditional expression is constant // warning C4714: function marked as __forceinline not inlined #pragma warning(push) #pragma warning(disable:4127 4714 6326) #endif template <class Backend, expression_template_option ExpressionTemplates> class number { typedef number<Backend, ExpressionTemplates> self_type; public: typedef Backend backend_type; BOOST_MP_FORCEINLINE BOOST_CONSTEXPR number() BOOST_MP_NOEXCEPT_IF(noexcept(Backend())) {} BOOST_MP_FORCEINLINE BOOST_CONSTEXPR number(const number& e) BOOST_MP_NOEXCEPT_IF(noexcept(Backend(std::declval<Backend const&>()))) : m_backend(e.m_backend){} template <class V> BOOST_MP_FORCEINLINE number(const V& v, typename boost::enable_if_c< (boost::is_arithmetic<V>::value || is_same<std::string, V>::value || is_convertible<V, const char*>::value) && !is_convertible<typename detail::canonical<V, Backend>::type, Backend>::value && !detail::is_restricted_conversion<typename detail::canonical<V, Backend>::type, Backend>::value >::type* = 0) { m_backend = canonical_value(v); } template <class V> BOOST_MP_FORCEINLINE BOOST_CONSTEXPR number(const V& v, typename boost::enable_if_c< is_convertible<typename detail::canonical<V, Backend>::type, Backend>::value && !detail::is_restricted_conversion<typename detail::canonical<V, Backend>::type, Backend>::value >::type* = 0) #ifndef BOOST_INTEL BOOST_MP_NOEXCEPT_IF(noexcept(Backend(std::declval<typename detail::canonical<V, Backend>::type const&>()))) #endif : m_backend(canonical_value(v)) {} BOOST_MP_FORCEINLINE BOOST_CONSTEXPR number(const number& e, unsigned digits10) BOOST_MP_NOEXCEPT_IF(noexcept(Backend(std::declval<Backend const&>(), std::declval<unsigned>()))) : m_backend(e.m_backend, digits10){} template <class V> explicit BOOST_MP_FORCEINLINE number(const V& v, typename boost::enable_if_c< (boost::is_arithmetic<V>::value || is_same<std::string, V>::value || is_convertible<V, const char*>::value) && !detail::is_explicitly_convertible<typename detail::canonical<V, Backend>::type, Backend>::value && detail::is_restricted_conversion<typename detail::canonical<V, Backend>::type, Backend>::value >::type* = 0) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<Backend&>() = std::declval<typename detail::canonical<V, Backend>::type const&>())) { m_backend = canonical_value(v); } template <class V> explicit BOOST_MP_FORCEINLINE BOOST_CONSTEXPR number(const V& v, typename boost::enable_if_c< detail::is_explicitly_convertible<typename detail::canonical<V, Backend>::type, Backend>::value && (detail::is_restricted_conversion<typename detail::canonical<V, Backend>::type, Backend>::value || !is_convertible<typename detail::canonical<V, Backend>::type, Backend>::value) >::type* = 0) BOOST_MP_NOEXCEPT_IF(noexcept(Backend(std::declval<typename detail::canonical<V, Backend>::type const&>()))) : m_backend(canonical_value(v)) {} /* // // This conflicts with component based initialization (for rational and complex types) // which is arguably more useful. Disabled for now. // template <class V> number(V v, unsigned digits10, typename boost::enable_if<mpl::or_<boost::is_arithmetic<V>, is_same<std::string, V>, is_convertible<V, const char*> > >::type* dummy1 = 0) { m_backend.precision(digits10); m_backend = canonical_value(v); } */ template<expression_template_option ET> BOOST_MP_FORCEINLINE BOOST_CONSTEXPR number(const number<Backend, ET>& val) BOOST_MP_NOEXCEPT_IF(noexcept(Backend(std::declval<Backend const&>()))) : m_backend(val.backend()) {} template <class Other, expression_template_option ET> BOOST_MP_FORCEINLINE number(const number<Other, ET>& val, typename boost::enable_if_c<(boost::is_convertible<Other, Backend>::value && !detail::is_restricted_conversion<Other, Backend>::value)>::type* = 0) BOOST_MP_NOEXCEPT_IF(noexcept(Backend(std::declval<Other const&>()))) : m_backend(val.backend()) {} template <class Other, expression_template_option ET> explicit number(const number<Other, ET>& val, typename boost::enable_if_c< (!detail::is_explicitly_convertible<Other, Backend>::value) >::type* = 0) { // // Attempt a generic interconvertion: // using detail::generic_interconvert; generic_interconvert(backend(), val.backend(), number_category<Backend>(), number_category<Other>()); } template <class Other, expression_template_option ET> explicit BOOST_MP_FORCEINLINE number(const number<Other, ET>& val, typename boost::enable_if_c< (detail::is_explicitly_convertible<Other, Backend>::value && (detail::is_restricted_conversion<Other, Backend>::value || !boost::is_convertible<Other, Backend>::value)) >::type* = 0) BOOST_MP_NOEXCEPT_IF(noexcept(Backend(std::declval<Other const&>()))) : m_backend(val.backend()) {} template <class V> BOOST_MP_FORCEINLINE number(V v1, V v2, typename boost::enable_if<mpl::or_<boost::is_arithmetic<V>, is_same<std::string, V>, is_convertible<V, const char*> > >::type* = 0) { using default_ops::assign_components; assign_components(m_backend, canonical_value(v1), canonical_value(v2)); } template <class Other, expression_template_option ET> BOOST_MP_FORCEINLINE number(const number<Other, ET>& v1, const number<Other, ET>& v2, typename boost::enable_if<boost::is_convertible<Other, Backend> >::type* = 0) { using default_ops::assign_components; assign_components(m_backend, v1.backend(), v2.backend()); } template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> typename boost::enable_if<is_convertible<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type, self_type>, number&>::type operator=(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& e) { typedef typename is_same<number, typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type>::type tag_type; do_assign(e, tag_type()); return *this; } template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> number& assign(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& e) { typedef typename is_same<number, typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type>::type tag_type; do_assign(e, tag_type()); return *this; } BOOST_MP_FORCEINLINE number& operator=(const number& e) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<Backend&>() = std::declval<Backend const&>())) { m_backend = e.m_backend; return *this; } template <class V> BOOST_MP_FORCEINLINE typename boost::enable_if<is_convertible<V, self_type>, number<Backend, ExpressionTemplates>& >::type operator=(const V& v) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<Backend&>() = std::declval<const typename detail::canonical<V, Backend>::type&>())) { m_backend = canonical_value(v); return *this; } template <class V> BOOST_MP_FORCEINLINE number<Backend, ExpressionTemplates>& assign(const V& v) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<Backend&>() = std::declval<const typename detail::canonical<V, Backend>::type&>())) { m_backend = canonical_value(v); return *this; } template <class Other, expression_template_option ET> typename boost::disable_if<boost::multiprecision::detail::is_explicitly_convertible<Other, Backend>, number<Backend, ExpressionTemplates>& >::type assign(const number<Other, ET>& v) { // // Attempt a generic interconvertion: // using detail::generic_interconvert; generic_interconvert(backend(), v.backend(), number_category<Backend>(), number_category<Other>()); return *this; } template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> number(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& e, typename boost::enable_if_c<is_convertible<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type, self_type>::value>::type* = 0) { *this = e; } template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> explicit number(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& e, typename boost::enable_if_c<!is_convertible<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type, self_type>::value && boost::multiprecision::detail::is_explicitly_convertible<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type, self_type>::value>::type* = 0) { assign(e); } #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES BOOST_MP_FORCEINLINE BOOST_CONSTEXPR number(number&& r) BOOST_MP_NOEXCEPT_IF(noexcept(Backend(std::declval<Backend>()))) : m_backend(static_cast<Backend&&>(r.m_backend)){} BOOST_MP_FORCEINLINE number& operator=(number&& r) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<Backend&>() = std::declval<Backend>())) { m_backend = static_cast<Backend&&>(r.m_backend); return *this; } #endif number& operator+=(const self_type& val) { do_add(detail::expression<detail::terminal, self_type>(val), detail::terminal()); return *this; } template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> typename boost::enable_if<is_convertible<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type, self_type>, number&>::type operator+=(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& e) { // Create a copy if e contains this, but not if we're just doing a // x += x if(contains_self(e) && !is_self(e)) { self_type temp(e); do_add(detail::expression<detail::terminal, self_type>(temp), detail::terminal()); } else { do_add(e, tag()); } return *this; } template <class Arg1, class Arg2, class Arg3, class Arg4> number& operator+=(const detail::expression<detail::multiply_immediates, Arg1, Arg2, Arg3, Arg4>& e) { // // Fused multiply-add: // using default_ops::eval_multiply_add; eval_multiply_add(m_backend, canonical_value(e.left_ref()), canonical_value(e.right_ref())); return *this; } template <class V> typename boost::enable_if<boost::is_convertible<V, self_type>, number<Backend, ExpressionTemplates>& >::type operator+=(const V& v) { using default_ops::eval_add; eval_add(m_backend, canonical_value(v)); return *this; } number& operator-=(const self_type& val) { do_subtract(detail::expression<detail::terminal, self_type>(val), detail::terminal()); return *this; } template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> typename boost::enable_if<is_convertible<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type, self_type>, number&>::type operator-=(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& e) { // Create a copy if e contains this: if(contains_self(e)) { self_type temp(e); do_subtract(detail::expression<detail::terminal, self_type>(temp), detail::terminal()); } else { do_subtract(e, typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::tag_type()); } return *this; } template <class V> typename boost::enable_if<boost::is_convertible<V, self_type>, number<Backend, ExpressionTemplates>& >::type operator-=(const V& v) { using default_ops::eval_subtract; eval_subtract(m_backend, canonical_value(v)); return *this; } template <class Arg1, class Arg2, class Arg3, class Arg4> number& operator-=(const detail::expression<detail::multiply_immediates, Arg1, Arg2, Arg3, Arg4>& e) { // // Fused multiply-subtract: // using default_ops::eval_multiply_subtract; eval_multiply_subtract(m_backend, canonical_value(e.left_ref()), canonical_value(e.right_ref())); return *this; } number& operator *= (const self_type& e) { do_multiplies(detail::expression<detail::terminal, self_type>(e), detail::terminal()); return *this; } template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> typename boost::enable_if<is_convertible<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type, self_type>, number&>::type operator*=(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& e) { // Create a temporary if the RHS references *this, but not // if we're just doing an x *= x; if(contains_self(e) && !is_self(e)) { self_type temp(e); do_multiplies(detail::expression<detail::terminal, self_type>(temp), detail::terminal()); } else { do_multiplies(e, typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::tag_type()); } return *this; } template <class V> typename boost::enable_if<boost::is_convertible<V, self_type>, number<Backend, ExpressionTemplates>& >::type operator*=(const V& v) { using default_ops::eval_multiply; eval_multiply(m_backend, canonical_value(v)); return *this; } number& operator%=(const self_type& e) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The modulus operation is only valid for integer types"); do_modulus(detail::expression<detail::terminal, self_type>(e), detail::terminal()); return *this; } template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> typename boost::enable_if<is_convertible<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type, self_type>, number&>::type operator%=(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& e) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The modulus operation is only valid for integer types"); // Create a temporary if the RHS references *this: if(contains_self(e)) { self_type temp(e); do_modulus(detail::expression<detail::terminal, self_type>(temp), detail::terminal()); } else { do_modulus(e, typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::tag_type()); } return *this; } template <class V> typename boost::enable_if<boost::is_convertible<V, self_type>, number<Backend, ExpressionTemplates>& >::type operator%=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The modulus operation is only valid for integer types"); using default_ops::eval_modulus; eval_modulus(m_backend, canonical_value(v)); return *this; } // // These operators are *not* proto-ized. // The issue is that the increment/decrement must happen // even if the result of the operator *is never used*. // Possibly we could modify our expression wrapper to // execute the increment/decrement on destruction, but // correct implementation will be tricky, so defered for now... // BOOST_MP_FORCEINLINE number& operator++() { using default_ops::eval_increment; eval_increment(m_backend); return *this; } BOOST_MP_FORCEINLINE number& operator--() { using default_ops::eval_decrement; eval_decrement(m_backend); return *this; } inline number operator++(int) { using default_ops::eval_increment; self_type temp(*this); eval_increment(m_backend); return BOOST_MP_MOVE(temp); } inline number operator--(int) { using default_ops::eval_decrement; self_type temp(*this); eval_decrement(m_backend); return BOOST_MP_MOVE(temp); } template <class V> BOOST_MP_FORCEINLINE typename boost::enable_if<is_integral<V>, number&>::type operator <<= (V val) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The left-shift operation is only valid for integer types"); detail::check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed<V>()); eval_left_shift(m_backend, static_cast<std::size_t>(canonical_value(val))); return *this; } template <class V> BOOST_MP_FORCEINLINE typename boost::enable_if<is_integral<V>, number&>::type operator >>= (V val) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The right-shift operation is only valid for integer types"); detail::check_shift_range(val, mpl::bool_<(sizeof(V) > sizeof(std::size_t))>(), is_signed<V>()); eval_right_shift(m_backend, static_cast<std::size_t>(canonical_value(val))); return *this; } BOOST_MP_FORCEINLINE number& operator /= (const self_type& e) { do_divide(detail::expression<detail::terminal, self_type>(e), detail::terminal()); return *this; } template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> typename boost::enable_if<is_convertible<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type, self_type>, number&>::type operator/=(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& e) { // Create a temporary if the RHS references *this: if(contains_self(e)) { self_type temp(e); do_divide(detail::expression<detail::terminal, self_type>(temp), detail::terminal()); } else { do_divide(e, typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::tag_type()); } return *this; } template <class V> BOOST_MP_FORCEINLINE typename boost::enable_if<boost::is_convertible<V, self_type>, number<Backend, ExpressionTemplates>& >::type operator/=(const V& v) { using default_ops::eval_divide; eval_divide(m_backend, canonical_value(v)); return *this; } BOOST_MP_FORCEINLINE number& operator&=(const self_type& e) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); do_bitwise_and(detail::expression<detail::terminal, self_type>(e), detail::terminal()); return *this; } template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> typename boost::enable_if<is_convertible<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type, self_type>, number&>::type operator&=(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& e) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); // Create a temporary if the RHS references *this, but not // if we're just doing an x &= x; if(contains_self(e) && !is_self(e)) { self_type temp(e); do_bitwise_and(detail::expression<detail::terminal, self_type>(temp), detail::terminal()); } else { do_bitwise_and(e, typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::tag_type()); } return *this; } template <class V> BOOST_MP_FORCEINLINE typename boost::enable_if<boost::is_convertible<V, self_type>, number<Backend, ExpressionTemplates>& >::type operator&=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); using default_ops::eval_bitwise_and; eval_bitwise_and(m_backend, canonical_value(v)); return *this; } BOOST_MP_FORCEINLINE number& operator|=(const self_type& e) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); do_bitwise_or(detail::expression<detail::terminal, self_type>(e), detail::terminal()); return *this; } template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> typename boost::enable_if<is_convertible<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type, self_type>, number&>::type operator|=(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& e) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); // Create a temporary if the RHS references *this, but not // if we're just doing an x |= x; if(contains_self(e) && !is_self(e)) { self_type temp(e); do_bitwise_or(detail::expression<detail::terminal, self_type>(temp), detail::terminal()); } else { do_bitwise_or(e, typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::tag_type()); } return *this; } template <class V> BOOST_MP_FORCEINLINE typename boost::enable_if<boost::is_convertible<V, self_type>, number<Backend, ExpressionTemplates>& >::type operator|=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); using default_ops::eval_bitwise_or; eval_bitwise_or(m_backend, canonical_value(v)); return *this; } BOOST_MP_FORCEINLINE number& operator^=(const self_type& e) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); do_bitwise_xor(detail::expression<detail::terminal, self_type>(e), detail::terminal()); return *this; } template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> typename boost::enable_if<is_convertible<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type, self_type>, number&>::type operator^=(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& e) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); if(contains_self(e)) { self_type temp(e); do_bitwise_xor(detail::expression<detail::terminal, self_type>(temp), detail::terminal()); } else { do_bitwise_xor(e, typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::tag_type()); } return *this; } template <class V> BOOST_MP_FORCEINLINE typename boost::enable_if<boost::is_convertible<V, self_type>, number<Backend, ExpressionTemplates>& >::type operator^=(const V& v) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); using default_ops::eval_bitwise_xor; eval_bitwise_xor(m_backend, canonical_value(v)); return *this; } // // swap: // BOOST_MP_FORCEINLINE void swap(self_type& other) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<Backend>().swap(std::declval<Backend&>()))) { m_backend.swap(other.backend()); } // // Zero and sign: // BOOST_MP_FORCEINLINE bool is_zero()const { using default_ops::eval_is_zero; return eval_is_zero(m_backend); } BOOST_MP_FORCEINLINE int sign()const { using default_ops::eval_get_sign; return eval_get_sign(m_backend); } // // String conversion functions: // std::string str(std::streamsize digits = 0, std::ios_base::fmtflags f = std::ios_base::fmtflags(0))const { return m_backend.str(digits, f); } template<class Archive> void serialize(Archive & ar, const unsigned int /*version*/) { ar & m_backend; } private: template <class T> void convert_to_imp(T* result)const { using default_ops::eval_convert_to; eval_convert_to(result, m_backend); } template <class B2, expression_template_option ET> void convert_to_imp(number<B2, ET>* result)const { result->assign(*this); } void convert_to_imp(std::string* result)const { *result = this->str(); } public: template <class T> T convert_to()const { T result; convert_to_imp(&result); return result; } // // Use in boolean context, and explicit conversion operators: // #ifndef BOOST_MP_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS # if (defined(__GNUC__) && (__GNUC__ == 4) && (__GNUC_MINOR__ < 7)) || (defined(BOOST_INTEL) && (BOOST_INTEL <= 1500)) // // Horrible workaround for gcc-4.6.x which always prefers the template // operator bool() rather than the non-template operator when converting to // an arithmetic type: // template <class T, typename boost::enable_if<is_same<T, bool>, int>::type = 0> explicit operator T ()const { using default_ops::eval_is_zero; return !eval_is_zero(backend()); } template <class T, typename boost::disable_if_c<is_same<T, bool>::value || is_void<T>::value, int>::type = 0> explicit operator T ()const { return this->template convert_to<T>(); } # else template <class T> explicit operator T()const { return this->template convert_to<T>(); } BOOST_MP_FORCEINLINE explicit operator bool()const { return !is_zero(); } #if BOOST_WORKAROUND(BOOST_GCC_VERSION, < 40800) BOOST_MP_FORCEINLINE explicit operator void()const {} #endif # endif #else typedef bool (self_type::*unmentionable_type)()const; BOOST_MP_FORCEINLINE operator unmentionable_type()const { return is_zero() ? 0 : &self_type::is_zero; } #endif // // Default precision: // static unsigned default_precision() BOOST_NOEXCEPT { return Backend::default_precision(); } static void default_precision(unsigned digits10) { Backend::default_precision(digits10); } unsigned precision()const BOOST_NOEXCEPT { return m_backend.precision(); } void precision(unsigned digits10) { m_backend.precision(digits10); } // // Comparison: // BOOST_MP_FORCEINLINE int compare(const number<Backend, ExpressionTemplates>& o)const BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<Backend>().compare(std::declval<Backend>()))) { return m_backend.compare(o.m_backend); } template <class V> BOOST_MP_FORCEINLINE typename boost::enable_if<is_arithmetic<V>, int>::type compare(const V& o)const { using default_ops::eval_get_sign; if(o == 0) return eval_get_sign(m_backend); return m_backend.compare(canonical_value(o)); } BOOST_MP_FORCEINLINE Backend& backend() BOOST_NOEXCEPT { return m_backend; } BOOST_MP_FORCEINLINE BOOST_CONSTEXPR const Backend& backend()const BOOST_NOEXCEPT { return m_backend; } private: template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> void do_assign(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& e, const mpl::true_&) { do_assign(e, tag()); } template <class tag, class Arg1, class Arg2, class Arg3, class Arg4> void do_assign(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& e, const mpl::false_&) { // The result of the expression isn't the same type as this - // create a temporary result and assign it to *this: typedef typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type temp_type; temp_type t(e); this->assign(t); } template <class Exp> void do_assign(const Exp& e, const detail::add_immediates&) { using default_ops::eval_add; eval_add(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template <class Exp> void do_assign(const Exp& e, const detail::subtract_immediates&) { using default_ops::eval_subtract; eval_subtract(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template <class Exp> void do_assign(const Exp& e, const detail::multiply_immediates&) { using default_ops::eval_multiply; eval_multiply(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template <class Exp> void do_assign(const Exp& e, const detail::multiply_add&) { using default_ops::eval_multiply_add; eval_multiply_add(m_backend, canonical_value(e.left().value()), canonical_value(e.middle().value()), canonical_value(e.right().value())); } template <class Exp> void do_assign(const Exp& e, const detail::multiply_subtract&) { using default_ops::eval_multiply_subtract; eval_multiply_subtract(m_backend, canonical_value(e.left().value()), canonical_value(e.middle().value()), canonical_value(e.right().value())); } template <class Exp> void do_assign(const Exp& e, const detail::divide_immediates&) { using default_ops::eval_divide; eval_divide(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template <class Exp> void do_assign(const Exp& e, const detail::negate&) { typedef typename Exp::left_type left_type; do_assign(e.left(), typename left_type::tag_type()); m_backend.negate(); } template <class Exp> void do_assign(const Exp& e, const detail::plus&) { typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; static int const left_depth = left_type::depth; static int const right_depth = right_type::depth; bool bl = contains_self(e.left()); bool br = contains_self(e.right()); if(bl && br) { self_type temp(e); temp.m_backend.swap(this->m_backend); } else if(bl && is_self(e.left())) { // Ignore the left node, it's *this, just add the right: do_add(e.right(), typename right_type::tag_type()); } else if(br && is_self(e.right())) { // Ignore the right node, it's *this, just add the left: do_add(e.left(), typename left_type::tag_type()); } else if(!br && (bl || (left_depth >= right_depth))) { // br is always false, but if bl is true we must take the this branch: do_assign(e.left(), typename left_type::tag_type()); do_add(e.right(), typename right_type::tag_type()); } else { do_assign(e.right(), typename right_type::tag_type()); do_add(e.left(), typename left_type::tag_type()); } } template <class Exp> void do_assign(const Exp& e, const detail::minus&) { typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; static int const left_depth = left_type::depth; static int const right_depth = right_type::depth; bool bl = contains_self(e.left()); bool br = contains_self(e.right()); if(bl && br) { self_type temp(e); temp.m_backend.swap(this->m_backend); } else if(bl && is_self(e.left())) { // Ignore the left node, it's *this, just subtract the right: do_subtract(e.right(), typename right_type::tag_type()); } else if(br && is_self(e.right())) { // Ignore the right node, it's *this, just subtract the left and negate the result: do_subtract(e.left(), typename left_type::tag_type()); m_backend.negate(); } else if(!br && (bl || (left_depth >= right_depth))) { // br is always false, but if bl is true we must take the this branch: do_assign(e.left(), typename left_type::tag_type()); do_subtract(e.right(), typename right_type::tag_type()); } else { do_assign(e.right(), typename right_type::tag_type()); do_subtract(e.left(), typename left_type::tag_type()); m_backend.negate(); } } template <class Exp> void do_assign(const Exp& e, const detail::multiplies&) { typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; static int const left_depth = left_type::depth; static int const right_depth = right_type::depth; bool bl = contains_self(e.left()); bool br = contains_self(e.right()); if(bl && br) { self_type temp(e); temp.m_backend.swap(this->m_backend); } else if(bl && is_self(e.left())) { // Ignore the left node, it's *this, just add the right: do_multiplies(e.right(), typename right_type::tag_type()); } else if(br && is_self(e.right())) { // Ignore the right node, it's *this, just add the left: do_multiplies(e.left(), typename left_type::tag_type()); } else if(!br && (bl || (left_depth >= right_depth))) { // br is always false, but if bl is true we must take the this branch: do_assign(e.left(), typename left_type::tag_type()); do_multiplies(e.right(), typename right_type::tag_type()); } else { do_assign(e.right(), typename right_type::tag_type()); do_multiplies(e.left(), typename left_type::tag_type()); } } template <class Exp> void do_assign(const Exp& e, const detail::divides&) { typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; bool bl = contains_self(e.left()); bool br = contains_self(e.right()); if(bl && is_self(e.left())) { // Ignore the left node, it's *this, just add the right: do_divide(e.right(), typename right_type::tag_type()); } else if(br) { self_type temp(e); temp.m_backend.swap(this->m_backend); } else { do_assign(e.left(), typename left_type::tag_type()); do_divide(e.right(), typename right_type::tag_type()); } } template <class Exp> void do_assign(const Exp& e, const detail::modulus&) { // // This operation is only valid for integer backends: // BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The modulus operation is only valid for integer types"); typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; bool bl = contains_self(e.left()); bool br = contains_self(e.right()); if(bl && is_self(e.left())) { // Ignore the left node, it's *this, just add the right: do_modulus(e.right(), typename right_type::tag_type()); } else if(br) { self_type temp(e); temp.m_backend.swap(this->m_backend); } else { do_assign(e.left(), typename left_type::tag_type()); do_modulus(e.right(), typename right_type::tag_type()); } } template <class Exp> void do_assign(const Exp& e, const detail::modulus_immediates&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The modulus operation is only valid for integer types"); using default_ops::eval_modulus; eval_modulus(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template <class Exp> void do_assign(const Exp& e, const detail::bitwise_and&) { // // This operation is only valid for integer backends: // BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "Bitwise operations are only valid for integer types"); typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; static int const left_depth = left_type::depth; static int const right_depth = right_type::depth; bool bl = contains_self(e.left()); bool br = contains_self(e.right()); if(bl && is_self(e.left())) { // Ignore the left node, it's *this, just add the right: do_bitwise_and(e.right(), typename right_type::tag_type()); } else if(br && is_self(e.right())) { do_bitwise_and(e.left(), typename left_type::tag_type()); } else if(!br && (bl || (left_depth >= right_depth))) { do_assign(e.left(), typename left_type::tag_type()); do_bitwise_and(e.right(), typename right_type::tag_type()); } else { do_assign(e.right(), typename right_type::tag_type()); do_bitwise_and(e.left(), typename left_type::tag_type()); } } template <class Exp> void do_assign(const Exp& e, const detail::bitwise_and_immediates&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "Bitwise operations are only valid for integer types"); using default_ops::eval_bitwise_and; eval_bitwise_and(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template <class Exp> void do_assign(const Exp& e, const detail::bitwise_or&) { // // This operation is only valid for integer backends: // BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "Bitwise operations are only valid for integer types"); typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; static int const left_depth = left_type::depth; static int const right_depth = right_type::depth; bool bl = contains_self(e.left()); bool br = contains_self(e.right()); if(bl && is_self(e.left())) { // Ignore the left node, it's *this, just add the right: do_bitwise_or(e.right(), typename right_type::tag_type()); } else if(br && is_self(e.right())) { do_bitwise_or(e.left(), typename left_type::tag_type()); } else if(!br && (bl || (left_depth >= right_depth))) { do_assign(e.left(), typename left_type::tag_type()); do_bitwise_or(e.right(), typename right_type::tag_type()); } else { do_assign(e.right(), typename right_type::tag_type()); do_bitwise_or(e.left(), typename left_type::tag_type()); } } template <class Exp> void do_assign(const Exp& e, const detail::bitwise_or_immediates&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "Bitwise operations are only valid for integer types"); using default_ops::eval_bitwise_or; eval_bitwise_or(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template <class Exp> void do_assign(const Exp& e, const detail::bitwise_xor&) { // // This operation is only valid for integer backends: // BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "Bitwise operations are only valid for integer types"); typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; static int const left_depth = left_type::depth; static int const right_depth = right_type::depth; bool bl = contains_self(e.left()); bool br = contains_self(e.right()); if(bl && is_self(e.left())) { // Ignore the left node, it's *this, just add the right: do_bitwise_xor(e.right(), typename right_type::tag_type()); } else if(br && is_self(e.right())) { do_bitwise_xor(e.left(), typename left_type::tag_type()); } else if(!br && (bl || (left_depth >= right_depth))) { do_assign(e.left(), typename left_type::tag_type()); do_bitwise_xor(e.right(), typename right_type::tag_type()); } else { do_assign(e.right(), typename right_type::tag_type()); do_bitwise_xor(e.left(), typename left_type::tag_type()); } } template <class Exp> void do_assign(const Exp& e, const detail::bitwise_xor_immediates&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "Bitwise operations are only valid for integer types"); using default_ops::eval_bitwise_xor; eval_bitwise_xor(m_backend, canonical_value(e.left().value()), canonical_value(e.right().value())); } template <class Exp> void do_assign(const Exp& e, const detail::terminal&) { if(!is_self(e)) { m_backend = canonical_value(e.value()); } } template <class Exp> void do_assign(const Exp& e, const detail::function&) { typedef typename Exp::arity tag_type; do_assign_function(e, tag_type()); } template <class Exp> void do_assign(const Exp& e, const detail::shift_left&) { // We can only shift by an integer value, not an arbitrary expression: typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; typedef typename right_type::arity right_arity; BOOST_STATIC_ASSERT_MSG(right_arity::value == 0, "The left shift operator requires an integer value for the shift operand."); typedef typename right_type::result_type right_value_type; BOOST_STATIC_ASSERT_MSG(is_integral<right_value_type>::value, "The left shift operator requires an integer value for the shift operand."); typedef typename left_type::tag_type tag_type; do_assign_left_shift(e.left(), canonical_value(e.right().value()), tag_type()); } template <class Exp> void do_assign(const Exp& e, const detail::shift_right&) { // We can only shift by an integer value, not an arbitrary expression: typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; typedef typename right_type::arity right_arity; BOOST_STATIC_ASSERT_MSG(right_arity::value == 0, "The left shift operator requires an integer value for the shift operand."); typedef typename right_type::result_type right_value_type; BOOST_STATIC_ASSERT_MSG(is_integral<right_value_type>::value, "The left shift operator requires an integer value for the shift operand."); typedef typename left_type::tag_type tag_type; do_assign_right_shift(e.left(), canonical_value(e.right().value()), tag_type()); } template <class Exp> void do_assign(const Exp& e, const detail::bitwise_complement&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise ~ operation is only valid for integer types"); using default_ops::eval_complement; self_type temp(e.left()); eval_complement(m_backend, temp.backend()); } template <class Exp> void do_assign(const Exp& e, const detail::complement_immediates&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise ~ operation is only valid for integer types"); using default_ops::eval_complement; eval_complement(m_backend, canonical_value(e.left().value())); } template <class Exp, class Val> void do_assign_right_shift(const Exp& e, const Val& val, const detail::terminal&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The right shift operation is only valid for integer types"); using default_ops::eval_right_shift; detail::check_shift_range(val, mpl::bool_<(sizeof(Val) > sizeof(std::size_t))>(), is_signed<Val>()); eval_right_shift(m_backend, canonical_value(e.value()), static_cast<std::size_t>(val)); } template <class Exp, class Val> void do_assign_left_shift(const Exp& e, const Val& val, const detail::terminal&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The left shift operation is only valid for integer types"); using default_ops::eval_left_shift; detail::check_shift_range(val, mpl::bool_<(sizeof(Val) > sizeof(std::size_t))>(), is_signed<Val>()); eval_left_shift(m_backend, canonical_value(e.value()), static_cast<std::size_t>(val)); } template <class Exp, class Val, class Tag> void do_assign_right_shift(const Exp& e, const Val& val, const Tag&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The right shift operation is only valid for integer types"); using default_ops::eval_right_shift; self_type temp(e); detail::check_shift_range(val, mpl::bool_<(sizeof(Val) > sizeof(std::size_t))>(), is_signed<Val>()); eval_right_shift(m_backend, temp.backend(), static_cast<std::size_t>(val)); } template <class Exp, class Val, class Tag> void do_assign_left_shift(const Exp& e, const Val& val, const Tag&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The left shift operation is only valid for integer types"); using default_ops::eval_left_shift; self_type temp(e); detail::check_shift_range(val, mpl::bool_<(sizeof(Val) > sizeof(std::size_t))>(), is_signed<Val>()); eval_left_shift(m_backend, temp.backend(), static_cast<std::size_t>(val)); } template <class Exp> void do_assign_function(const Exp& e, const mpl::int_<1>&) { e.left().value()(&m_backend); } template <class Exp> void do_assign_function(const Exp& e, const mpl::int_<2>&) { typedef typename Exp::right_type right_type; typedef typename right_type::tag_type tag_type; do_assign_function_1(e.left().value(), e.right_ref(), tag_type()); } template <class F, class Exp> void do_assign_function_1(const F& f, const Exp& val, const detail::terminal&) { f(m_backend, function_arg_value(val)); } template <class F, class Exp, class Tag> void do_assign_function_1(const F& f, const Exp& val, const Tag&) { number t(val); f(m_backend, t.backend()); } template <class Exp> void do_assign_function(const Exp& e, const mpl::int_<3>&) { typedef typename Exp::middle_type middle_type; typedef typename middle_type::tag_type tag_type; typedef typename Exp::right_type end_type; typedef typename end_type::tag_type end_tag; do_assign_function_2(e.left().value(), e.middle_ref(), e.right_ref(), tag_type(), end_tag()); } template <class F, class Exp1, class Exp2> void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const detail::terminal&, const detail::terminal&) { f(m_backend, function_arg_value(val1), function_arg_value(val2)); } template <class F, class Exp1, class Exp2, class Tag1> void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const detail::terminal&) { self_type temp1(val1); f(m_backend, BOOST_MP_MOVE(temp1.backend()), function_arg_value(val2)); } template <class F, class Exp1, class Exp2, class Tag2> void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const detail::terminal&, const Tag2&) { self_type temp2(val2); f(m_backend, function_arg_value(val1), BOOST_MP_MOVE(temp2.backend())); } template <class F, class Exp1, class Exp2, class Tag1, class Tag2> void do_assign_function_2(const F& f, const Exp1& val1, const Exp2& val2, const Tag1&, const Tag2&) { self_type temp1(val1); self_type temp2(val2); f(m_backend, BOOST_MP_MOVE(temp1.backend()), BOOST_MP_MOVE(temp2.backend())); } template <class Exp> void do_assign_function(const Exp& e, const mpl::int_<4>&) { typedef typename Exp::left_middle_type left_type; typedef typename left_type::tag_type left_tag_type; typedef typename Exp::right_middle_type middle_type; typedef typename middle_type::tag_type middle_tag_type; typedef typename Exp::right_type right_type; typedef typename right_type::tag_type right_tag_type; do_assign_function_3a(e.left().value(), e.left_middle_ref(), e.right_middle_ref(), e.right_ref(), left_tag_type(), middle_tag_type(), right_tag_type()); } template <class F, class Exp1, class Exp2, class Exp3, class Tag2, class Tag3> void do_assign_function_3a(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const detail::terminal&, const Tag2& t2, const Tag3& t3) { do_assign_function_3b(f, val1, val2, val3, t2, t3); } template <class F, class Exp1, class Exp2, class Exp3, class Tag1, class Tag2, class Tag3> void do_assign_function_3a(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const Tag1&, const Tag2& t2, const Tag3& t3) { number t(val1); do_assign_function_3b(f, BOOST_MP_MOVE(t), val2, val3, t2, t3); } template <class F, class Exp1, class Exp2, class Exp3, class Tag3> void do_assign_function_3b(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const detail::terminal&, const Tag3& t3) { do_assign_function_3c(f, val1, val2, val3, t3); } template <class F, class Exp1, class Exp2, class Exp3, class Tag2, class Tag3> void do_assign_function_3b(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const Tag2& /*t2*/, const Tag3& t3) { number t(val2); do_assign_function_3c(f, val1, BOOST_MP_MOVE(t), val3, t3); } template <class F, class Exp1, class Exp2, class Exp3> void do_assign_function_3c(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const detail::terminal&) { f(m_backend, function_arg_value(val1), function_arg_value(val2), function_arg_value(val3)); } template <class F, class Exp1, class Exp2, class Exp3, class Tag3> void do_assign_function_3c(const F& f, const Exp1& val1, const Exp2& val2, const Exp3& val3, const Tag3& /*t3*/) { number t(val3); do_assign_function_3c(f, val1, val2, BOOST_MP_MOVE(t), detail::terminal()); } template <class Exp> void do_add(const Exp& e, const detail::terminal&) { using default_ops::eval_add; eval_add(m_backend, canonical_value(e.value())); } template <class Exp> void do_add(const Exp& e, const detail::negate&) { typedef typename Exp::left_type left_type; do_subtract(e.left(), typename left_type::tag_type()); } template <class Exp> void do_add(const Exp& e, const detail::plus&) { typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; do_add(e.left(), typename left_type::tag_type()); do_add(e.right(), typename right_type::tag_type()); } template <class Exp> void do_add(const Exp& e, const detail::minus&) { typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; do_add(e.left(), typename left_type::tag_type()); do_subtract(e.right(), typename right_type::tag_type()); } template <class Exp, class unknown> void do_add(const Exp& e, const unknown&) { self_type temp(e); do_add(detail::expression<detail::terminal, self_type>(temp), detail::terminal()); } template <class Exp> void do_add(const Exp& e, const detail::add_immediates&) { using default_ops::eval_add; eval_add(m_backend, canonical_value(e.left().value())); eval_add(m_backend, canonical_value(e.right().value())); } template <class Exp> void do_add(const Exp& e, const detail::subtract_immediates&) { using default_ops::eval_add; using default_ops::eval_subtract; eval_add(m_backend, canonical_value(e.left().value())); eval_subtract(m_backend, canonical_value(e.right().value())); } template <class Exp> void do_subtract(const Exp& e, const detail::terminal&) { using default_ops::eval_subtract; eval_subtract(m_backend, canonical_value(e.value())); } template <class Exp> void do_subtract(const Exp& e, const detail::negate&) { typedef typename Exp::left_type left_type; do_add(e.left(), typename left_type::tag_type()); } template <class Exp> void do_subtract(const Exp& e, const detail::plus&) { typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; do_subtract(e.left(), typename left_type::tag_type()); do_subtract(e.right(), typename right_type::tag_type()); } template <class Exp> void do_subtract(const Exp& e, const detail::minus&) { typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; do_subtract(e.left(), typename left_type::tag_type()); do_add(e.right(), typename right_type::tag_type()); } template <class Exp> void do_subtract(const Exp& e, const detail::add_immediates&) { using default_ops::eval_subtract; eval_subtract(m_backend, canonical_value(e.left().value())); eval_subtract(m_backend, canonical_value(e.right().value())); } template <class Exp> void do_subtract(const Exp& e, const detail::subtract_immediates&) { using default_ops::eval_add; using default_ops::eval_subtract; eval_subtract(m_backend, canonical_value(e.left().value())); eval_add(m_backend, canonical_value(e.right().value())); } template <class Exp, class unknown> void do_subtract(const Exp& e, const unknown&) { self_type temp(e); do_subtract(detail::expression<detail::terminal, self_type>(temp), detail::terminal()); } template <class Exp> void do_multiplies(const Exp& e, const detail::terminal&) { using default_ops::eval_multiply; eval_multiply(m_backend, canonical_value(e.value())); } template <class Exp> void do_multiplies(const Exp& e, const detail::negate&) { typedef typename Exp::left_type left_type; do_multiplies(e.left(), typename left_type::tag_type()); m_backend.negate(); } template <class Exp> void do_multiplies(const Exp& e, const detail::multiplies&) { typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; do_multiplies(e.left(), typename left_type::tag_type()); do_multiplies(e.right(), typename right_type::tag_type()); } // // This rearrangement is disabled for integer types, the test on sizeof(Exp) is simply to make // the disable_if dependent on the template argument (the size of 1 can never occur in practice). // template <class Exp> typename boost::disable_if_c<boost::multiprecision::number_category<self_type>::value == boost::multiprecision::number_kind_integer || sizeof(Exp) == 1>::type do_multiplies(const Exp& e, const detail::divides&) { typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; do_multiplies(e.left(), typename left_type::tag_type()); do_divide(e.right(), typename right_type::tag_type()); } template <class Exp> void do_multiplies(const Exp& e, const detail::multiply_immediates&) { using default_ops::eval_multiply; eval_multiply(m_backend, canonical_value(e.left().value())); eval_multiply(m_backend, canonical_value(e.right().value())); } // // This rearrangement is disabled for integer types, the test on sizeof(Exp) is simply to make // the disable_if dependent on the template argument (the size of 1 can never occur in practice). // template <class Exp> typename boost::disable_if_c<boost::multiprecision::number_category<self_type>::value == boost::multiprecision::number_kind_integer || sizeof(Exp) == 1>::type do_multiplies(const Exp& e, const detail::divide_immediates&) { using default_ops::eval_multiply; using default_ops::eval_divide; eval_multiply(m_backend, canonical_value(e.left().value())); eval_divide(m_backend, canonical_value(e.right().value())); } template <class Exp, class unknown> void do_multiplies(const Exp& e, const unknown&) { using default_ops::eval_multiply; self_type temp(e); eval_multiply(m_backend, temp.m_backend); } template <class Exp> void do_divide(const Exp& e, const detail::terminal&) { using default_ops::eval_divide; eval_divide(m_backend, canonical_value(e.value())); } template <class Exp> void do_divide(const Exp& e, const detail::negate&) { typedef typename Exp::left_type left_type; do_divide(e.left(), typename left_type::tag_type()); m_backend.negate(); } // // This rearrangement is disabled for integer types, the test on sizeof(Exp) is simply to make // the disable_if dependent on the template argument (the size of 1 can never occur in practice). // template <class Exp> typename boost::disable_if_c<boost::multiprecision::number_category<self_type>::value == boost::multiprecision::number_kind_integer || sizeof(Exp) == 1>::type do_divide(const Exp& e, const detail::multiplies&) { typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; do_divide(e.left(), typename left_type::tag_type()); do_divide(e.right(), typename right_type::tag_type()); } // // This rearrangement is disabled for integer types, the test on sizeof(Exp) is simply to make // the disable_if dependent on the template argument (the size of 1 can never occur in practice). // template <class Exp> typename boost::disable_if_c<boost::multiprecision::number_category<self_type>::value == boost::multiprecision::number_kind_integer || sizeof(Exp) == 1>::type do_divide(const Exp& e, const detail::divides&) { typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; do_divide(e.left(), typename left_type::tag_type()); do_multiplies(e.right(), typename right_type::tag_type()); } // // This rearrangement is disabled for integer types, the test on sizeof(Exp) is simply to make // the disable_if dependent on the template argument (the size of 1 can never occur in practice). // template <class Exp> typename boost::disable_if_c<boost::multiprecision::number_category<self_type>::value == boost::multiprecision::number_kind_integer || sizeof(Exp) == 1>::type do_divides(const Exp& e, const detail::multiply_immediates&) { using default_ops::eval_divide; eval_divide(m_backend, canonical_value(e.left().value())); eval_divide(m_backend, canonical_value(e.right().value())); } // // This rearrangement is disabled for integer types, the test on sizeof(Exp) is simply to make // the disable_if dependent on the template argument (the size of 1 can never occur in practice). // template <class Exp> typename boost::disable_if_c<boost::multiprecision::number_category<self_type>::value == boost::multiprecision::number_kind_integer || sizeof(Exp) == 1>::type do_divides(const Exp& e, const detail::divide_immediates&) { using default_ops::eval_multiply; using default_ops::eval_divide; eval_divide(m_backend, canonical_value(e.left().value())); mutiply(m_backend, canonical_value(e.right().value())); } template <class Exp, class unknown> void do_divide(const Exp& e, const unknown&) { using default_ops::eval_multiply; self_type temp(e); eval_divide(m_backend, temp.m_backend); } template <class Exp> void do_modulus(const Exp& e, const detail::terminal&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The modulus operation is only valid for integer types"); using default_ops::eval_modulus; eval_modulus(m_backend, canonical_value(e.value())); } template <class Exp, class Unknown> void do_modulus(const Exp& e, const Unknown&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The modulus operation is only valid for integer types"); using default_ops::eval_modulus; self_type temp(e); eval_modulus(m_backend, canonical_value(temp)); } template <class Exp> void do_bitwise_and(const Exp& e, const detail::terminal&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); using default_ops::eval_bitwise_and; eval_bitwise_and(m_backend, canonical_value(e.value())); } template <class Exp> void do_bitwise_and(const Exp& e, const detail::bitwise_and&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; do_bitwise_and(e.left(), typename left_type::tag_type()); do_bitwise_and(e.right(), typename right_type::tag_type()); } template <class Exp, class unknown> void do_bitwise_and(const Exp& e, const unknown&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise & operation is only valid for integer types"); using default_ops::eval_bitwise_and; self_type temp(e); eval_bitwise_and(m_backend, temp.m_backend); } template <class Exp> void do_bitwise_or(const Exp& e, const detail::terminal&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); using default_ops::eval_bitwise_or; eval_bitwise_or(m_backend, canonical_value(e.value())); } template <class Exp> void do_bitwise_or(const Exp& e, const detail::bitwise_or&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; do_bitwise_or(e.left(), typename left_type::tag_type()); do_bitwise_or(e.right(), typename right_type::tag_type()); } template <class Exp, class unknown> void do_bitwise_or(const Exp& e, const unknown&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise | operation is only valid for integer types"); using default_ops::eval_bitwise_or; self_type temp(e); eval_bitwise_or(m_backend, temp.m_backend); } template <class Exp> void do_bitwise_xor(const Exp& e, const detail::terminal&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); using default_ops::eval_bitwise_xor; eval_bitwise_xor(m_backend, canonical_value(e.value())); } template <class Exp> void do_bitwise_xor(const Exp& e, const detail::bitwise_xor&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); typedef typename Exp::left_type left_type; typedef typename Exp::right_type right_type; do_bitwise_xor(e.left(), typename left_type::tag_type()); do_bitwise_xor(e.right(), typename right_type::tag_type()); } template <class Exp, class unknown> void do_bitwise_xor(const Exp& e, const unknown&) { BOOST_STATIC_ASSERT_MSG(number_category<Backend>::value == number_kind_integer, "The bitwise ^ operation is only valid for integer types"); using default_ops::eval_bitwise_xor; self_type temp(e); eval_bitwise_xor(m_backend, temp.m_backend); } // Tests if the expression contains a reference to *this: template <class Exp> BOOST_MP_FORCEINLINE bool contains_self(const Exp& e)const BOOST_NOEXCEPT { return contains_self(e, typename Exp::arity()); } template <class Exp> BOOST_MP_FORCEINLINE bool contains_self(const Exp& e, mpl::int_<0> const&)const BOOST_NOEXCEPT { return is_realy_self(e.value()); } template <class Exp> BOOST_MP_FORCEINLINE bool contains_self(const Exp& e, mpl::int_<1> const&)const BOOST_NOEXCEPT { typedef typename Exp::left_type child_type; return contains_self(e.left(), typename child_type::arity()); } template <class Exp> BOOST_MP_FORCEINLINE bool contains_self(const Exp& e, mpl::int_<2> const&)const BOOST_NOEXCEPT { typedef typename Exp::left_type child0_type; typedef typename Exp::right_type child1_type; return contains_self(e.left(), typename child0_type::arity()) || contains_self(e.right(), typename child1_type::arity()); } template <class Exp> BOOST_MP_FORCEINLINE bool contains_self(const Exp& e, mpl::int_<3> const&)const BOOST_NOEXCEPT { typedef typename Exp::left_type child0_type; typedef typename Exp::middle_type child1_type; typedef typename Exp::right_type child2_type; return contains_self(e.left(), typename child0_type::arity()) || contains_self(e.middle(), typename child1_type::arity()) || contains_self(e.right(), typename child2_type::arity()); } // Test if the expression is a reference to *this: template <class Exp> BOOST_MP_FORCEINLINE BOOST_CONSTEXPR bool is_self(const Exp& e)const BOOST_NOEXCEPT { return is_self(e, typename Exp::arity()); } template <class Exp> BOOST_MP_FORCEINLINE BOOST_CONSTEXPR bool is_self(const Exp& e, mpl::int_<0> const&)const BOOST_NOEXCEPT { return is_realy_self(e.value()); } template <class Exp, int v> BOOST_MP_FORCEINLINE BOOST_CONSTEXPR bool is_self(const Exp&, mpl::int_<v> const&)const BOOST_NOEXCEPT { return false; } template <class Val> BOOST_MP_FORCEINLINE BOOST_CONSTEXPR bool is_realy_self(const Val&)const BOOST_NOEXCEPT{ return false; } BOOST_MP_FORCEINLINE BOOST_CONSTEXPR bool is_realy_self(const self_type& v)const BOOST_NOEXCEPT{ return &v == this; } static BOOST_MP_FORCEINLINE BOOST_CONSTEXPR const Backend& function_arg_value(const self_type& v) BOOST_NOEXCEPT { return v.backend(); } template <class V> static BOOST_MP_FORCEINLINE BOOST_CONSTEXPR const V& function_arg_value(const V& v) BOOST_NOEXCEPT { return v; } template <class A1, class A2, class A3, class A4> static BOOST_MP_FORCEINLINE const A1& function_arg_value(const detail::expression<detail::terminal, A1, A2, A3, A4>& exp) BOOST_NOEXCEPT { return exp.value(); } template <class A2, class A3, class A4> static BOOST_MP_FORCEINLINE BOOST_CONSTEXPR const Backend& function_arg_value(const detail::expression<detail::terminal, number<Backend>, A2, A3, A4>& exp) BOOST_NOEXCEPT { return exp.value().backend(); } Backend m_backend; public: // // These shouldn't really need to be public, or even member functions, but it makes implementing // the non-member operators way easier if they are: // static BOOST_MP_FORCEINLINE BOOST_CONSTEXPR const Backend& canonical_value(const self_type& v) BOOST_NOEXCEPT { return v.m_backend; } template <class B2, expression_template_option ET> static BOOST_MP_FORCEINLINE BOOST_CONSTEXPR const B2& canonical_value(const number<B2, ET>& v) BOOST_NOEXCEPT { return v.backend(); } template <class V> static BOOST_MP_FORCEINLINE BOOST_CONSTEXPR typename boost::disable_if<is_same<typename detail::canonical<V, Backend>::type, V>, typename detail::canonical<V, Backend>::type>::type canonical_value(const V& v) BOOST_NOEXCEPT { return static_cast<typename detail::canonical<V, Backend>::type>(v); } template <class V> static BOOST_MP_FORCEINLINE BOOST_CONSTEXPR typename boost::enable_if<is_same<typename detail::canonical<V, Backend>::type, V>, const V&>::type canonical_value(const V& v) BOOST_NOEXCEPT { return v; } static BOOST_MP_FORCEINLINE typename detail::canonical<std::string, Backend>::type canonical_value(const std::string& v) BOOST_NOEXCEPT { return v.c_str(); } }; template <class Backend, expression_template_option ExpressionTemplates> inline std::ostream& operator << (std::ostream& os, const number<Backend, ExpressionTemplates>& r) { std::streamsize d = os.precision(); std::string s = r.str(d, os.flags()); std::streamsize ss = os.width(); if(ss > static_cast<std::streamsize>(s.size())) { char fill = os.fill(); if((os.flags() & std::ios_base::left) == std::ios_base::left) s.append(static_cast<std::string::size_type>(ss - s.size()), fill); else s.insert(static_cast<std::string::size_type>(0), static_cast<std::string::size_type>(ss - s.size()), fill); } return os << s; } namespace detail{ template <class tag, class A1, class A2, class A3, class A4> inline std::ostream& operator << (std::ostream& os, const expression<tag, A1, A2, A3, A4>& r) { typedef typename expression<tag, A1, A2, A3, A4>::result_type value_type; value_type temp(r); return os << temp; } // // What follows is the input streaming code: this is not "proper" iostream code at all // but that's fiendishly hard to write when dealing with multiple backends all // with different requirements... yes we could deligate this to the backend author... // but we really want backends to be EASY to write! // For now just pull in all the characters that could possibly form the number // and let the backend's string parser make use of it. This fixes most use cases // including CSV type formats such as those used by the Random lib. // inline std::string read_string_while(std::istream& is, std::string const& permitted_chars) { std::ios_base::iostate state = std::ios_base::goodbit; const std::istream::sentry sentry_check(is); std::string result; if(sentry_check) { int c = is.rdbuf()->sgetc(); for(;; c = is.rdbuf()->snextc()) if(std::istream::traits_type::eq_int_type(std::istream::traits_type::eof(), c)) { // end of file: state |= std::ios_base::eofbit; break; } else if(permitted_chars.find_first_of(std::istream::traits_type::to_char_type(c)) == std::string::npos) { // Invalid numeric character, stop reading: //is.rdbuf()->sputbackc(static_cast<char>(c)); break; } else { result.append(1, std::istream::traits_type::to_char_type(c)); } } if(!result.size()) state |= std::ios_base::failbit; is.setstate(state); return result; } } // namespace detail template <class Backend, expression_template_option ExpressionTemplates> inline std::istream& operator >> (std::istream& is, number<Backend, ExpressionTemplates>& r) { bool hex_format = (is.flags() & std::ios_base::hex) == std::ios_base::hex; bool oct_format = (is.flags() & std::ios_base::oct) == std::ios_base::oct; std::string s; switch(boost::multiprecision::number_category<number<Backend, ExpressionTemplates> >::value) { case boost::multiprecision::number_kind_integer: if(oct_format) s = detail::read_string_while(is, "+-01234567"); else if(hex_format) s = detail::read_string_while(is, "+-xXabcdefABCDEF0123456789"); else s = detail::read_string_while(is, "+-0123456789"); break; case boost::multiprecision::number_kind_floating_point: s = detail::read_string_while(is, "+-eE.0123456789infINFnanNANinfinityINFINITY"); break; default: is >> s; } if(s.size()) { if(hex_format && (number_category<Backend>::value == number_kind_integer) && ((s[0] != '0') || (s[1] != 'x'))) s.insert(s.find_first_not_of("+-"), "0x"); if(oct_format && (number_category<Backend>::value == number_kind_integer) && (s[0] != '0')) s.insert(s.find_first_not_of("+-"), "0"); r.assign(s); } else if(!is.fail()) is.setstate(std::istream::failbit); return is; } template <class Backend, expression_template_option ExpressionTemplates> BOOST_MP_FORCEINLINE void swap(number<Backend, ExpressionTemplates>& a, number<Backend, ExpressionTemplates>& b) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<number<Backend, ExpressionTemplates>&>() = std::declval<number<Backend, ExpressionTemplates>&>())) { a.swap(b); } // // Boost.Hash support, just call hash_value for the backend, which may or may not be supported: // template <class Backend, expression_template_option ExpressionTemplates> inline std::size_t hash_value(const number<Backend, ExpressionTemplates>& val) { return hash_value(val.backend()); } } // namespace multiprecision template <class T> class rational; template <class Backend, multiprecision::expression_template_option ExpressionTemplates> inline std::istream& operator >> (std::istream& is, rational<multiprecision::number<Backend, ExpressionTemplates> >& r) { std::string s1; multiprecision::number<Backend, ExpressionTemplates> v1, v2; char c; bool have_hex = false; bool hex_format = (is.flags() & std::ios_base::hex) == std::ios_base::hex; bool oct_format = (is.flags() & std::ios_base::oct) == std::ios_base::oct; while((EOF != (c = static_cast<char>(is.peek()))) && (c == 'x' || c == 'X' || c == '-' || c == '+' || (c >= '0' && c <= '9') || (have_hex && (c >= 'a' && c <= 'f')) || (have_hex && (c >= 'A' && c <= 'F')))) { if(c == 'x' || c == 'X') have_hex = true; s1.append(1, c); is.get(); } if(hex_format && ((s1[0] != '0') || (s1[1] != 'x'))) s1.insert(static_cast<std::string::size_type>(0), "0x"); if(oct_format && (s1[0] != '0')) s1.insert(static_cast<std::string::size_type>(0), "0"); v1.assign(s1); s1.erase(); if(c == '/') { is.get(); while((EOF != (c = static_cast<char>(is.peek()))) && (c == 'x' || c == 'X' || c == '-' || c == '+' || (c >= '0' && c <= '9') || (have_hex && (c >= 'a' && c <= 'f')) || (have_hex && (c >= 'A' && c <= 'F')))) { if(c == 'x' || c == 'X') have_hex = true; s1.append(1, c); is.get(); } if(hex_format && ((s1[0] != '0') || (s1[1] != 'x'))) s1.insert(static_cast<std::string::size_type>(0), "0x"); if(oct_format && (s1[0] != '0')) s1.insert(static_cast<std::string::size_type>(0), "0"); v2.assign(s1); } else v2 = 1; r.assign(v1, v2); return is; } template <class T, multiprecision::expression_template_option ExpressionTemplates> inline multiprecision::number<T, ExpressionTemplates> numerator(const rational<multiprecision::number<T, ExpressionTemplates> >& a) { return a.numerator(); } template <class T, multiprecision::expression_template_option ExpressionTemplates> inline multiprecision::number<T, ExpressionTemplates> denominator(const rational<multiprecision::number<T, ExpressionTemplates> >& a) { return a.denominator(); } namespace multiprecision { template <class I> struct component_type<boost::rational<I> > { typedef I type; }; } #ifdef BOOST_MSVC #pragma warning(pop) #endif } // namespaces #ifndef BOOST_NO_CXX11_HDR_FUNCTIONAL #include <functional> namespace std { template <class Backend, boost::multiprecision::expression_template_option ExpressionTemplates> struct hash<boost::multiprecision::number<Backend, ExpressionTemplates> > { std::size_t operator()(const boost::multiprecision::number<Backend, ExpressionTemplates>& val)const { return hash_value(val); } }; } #endif #include <boost/multiprecision/detail/ublas_interop.hpp> #endif