/////////////////////////////////////////////////////////////// // Copyright 2012 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_ #ifndef BOOST_MATH_FLOAT_BACKEND_HPP #define BOOST_MATH_FLOAT_BACKEND_HPP #include <iostream> #include <iomanip> #include <sstream> #include <boost/cstdint.hpp> #include <boost/lexical_cast.hpp> #include <boost/math/concepts/real_concept.hpp> #include <boost/multiprecision/number.hpp> #include <boost/math/common_factor_rt.hpp> namespace boost{ namespace multiprecision{ namespace backends{ #ifdef BOOST_MSVC # pragma warning(push) # pragma warning(disable:4389 4244 4018 4244 4127) #endif template <class Arithmetic> struct arithmetic_backend { typedef mpl::list<short, int, long, long long> signed_types; typedef mpl::list<unsigned short, unsigned, unsigned long, unsigned long long> unsigned_types; typedef mpl::list<float, double, long double> float_types; typedef int exponent_type; arithmetic_backend(){} arithmetic_backend(const arithmetic_backend& o) { m_value = o.m_value; } template <class A> arithmetic_backend(const A& o, const typename enable_if<is_arithmetic<A> >::type* = 0) : m_value(o) {} template <class A> arithmetic_backend(const arithmetic_backend<A>& o) : m_value(o.data()) {} arithmetic_backend& operator = (const arithmetic_backend& o) { m_value = o.m_value; return *this; } template <class A> typename enable_if<is_arithmetic<A>, arithmetic_backend&>::type operator = (A i) { m_value = i; return *this; } template <class A> arithmetic_backend& operator = (const arithmetic_backend<A>& i) { m_value = i.data(); return *this; } arithmetic_backend& operator = (const char* s) { try { m_value = boost::lexical_cast<Arithmetic>(s); } catch(const bad_lexical_cast&) { throw std::runtime_error(std::string("Unable to interpret the string provided: \"") + s + std::string("\" as a compatible number type.")); } return *this; } void swap(arithmetic_backend& o) { std::swap(m_value, o.m_value); } std::string str(std::streamsize digits, std::ios_base::fmtflags f)const { std::stringstream ss; ss.flags(f); ss << std::setprecision(digits ? digits : std::numeric_limits<Arithmetic>::digits10 + 4) << m_value; return ss.str(); } void do_negate(const mpl::true_&) { m_value = 1 + ~m_value; } void do_negate(const mpl::false_&) { m_value = -m_value; } void negate() { do_negate(is_unsigned<Arithmetic>()); } int compare(const arithmetic_backend& o)const { return m_value > o.m_value ? 1 : (m_value < o.m_value ? -1 : 0); } template <class A> typename enable_if<is_arithmetic<A>, int>::type compare(A i)const { return m_value > static_cast<Arithmetic>(i) ? 1 : (m_value < static_cast<Arithmetic>(i) ? -1 : 0); } Arithmetic& data() { return m_value; } const Arithmetic& data()const { return m_value; } private: Arithmetic m_value; }; template <class R, class Arithmetic> inline void eval_convert_to(R* result, const arithmetic_backend<Arithmetic>& backend) { *result = backend.data(); } template <class Arithmetic> inline bool eval_eq(const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) { return a.data() == b.data(); } template <class Arithmetic, class A2> inline typename enable_if<is_arithmetic<A2>, bool>::type eval_eq(const arithmetic_backend<Arithmetic>& a, const A2& b) { return a.data() == static_cast<Arithmetic>(b); } template <class Arithmetic> inline bool eval_lt(const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) { return a.data() < b.data(); } template <class Arithmetic, class A2> inline typename enable_if<is_arithmetic<A2>, bool>::type eval_lt(const arithmetic_backend<Arithmetic>& a, const A2& b) { return a.data() < static_cast<Arithmetic>(b); } template <class Arithmetic> inline bool eval_gt(const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) { return a.data() > b.data(); } template <class Arithmetic, class A2> inline typename enable_if<is_arithmetic<A2>, bool>::type eval_gt(const arithmetic_backend<Arithmetic>& a, const A2& b) { return a.data() > static_cast<Arithmetic>(b); } template <class Arithmetic> inline void eval_add(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { result.data() += o.data(); } template <class Arithmetic> inline void eval_subtract(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { result.data() -= o.data(); } template <class Arithmetic> inline void eval_multiply(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { result.data() *= o.data(); } template <class Arithmetic> inline typename enable_if_c<std::numeric_limits<Arithmetic>::has_infinity>::type eval_divide(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { result.data() /= o.data(); } template <class Arithmetic> inline typename disable_if_c<std::numeric_limits<Arithmetic>::has_infinity>::type eval_divide(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { if(!o.data()) BOOST_THROW_EXCEPTION(std::overflow_error("Divide by zero")); result.data() /= o.data(); } template <class Arithmetic, class A2> inline typename enable_if<is_arithmetic<A2> >::type eval_add(arithmetic_backend<Arithmetic>& result, const A2& o) { result.data() += o; } template <class Arithmetic, class A2> inline typename enable_if<is_arithmetic<A2> >::type eval_subtract(arithmetic_backend<Arithmetic>& result, const A2& o) { result.data() -= o; } template <class Arithmetic, class A2> inline typename enable_if<is_arithmetic<A2> >::type eval_multiply(arithmetic_backend<Arithmetic>& result, const A2& o) { result.data() *= o; } template <class Arithmetic, class A2> inline typename enable_if_c<(is_arithmetic<A2>::value && !std::numeric_limits<Arithmetic>::has_infinity)>::type eval_divide(arithmetic_backend<Arithmetic>& result, const A2& o) { if(!o) BOOST_THROW_EXCEPTION(std::overflow_error("Divide by zero")); result.data() /= o; } template <class Arithmetic, class A2> inline typename enable_if_c<(is_arithmetic<A2>::value && std::numeric_limits<Arithmetic>::has_infinity)>::type eval_divide(arithmetic_backend<Arithmetic>& result, const A2& o) { result.data() /= o; } template <class Arithmetic> inline void eval_add(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) { result.data() = a.data() + b.data(); } template <class Arithmetic> inline void eval_subtract(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) { result.data() = a.data() - b.data(); } template <class Arithmetic> inline void eval_multiply(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) { result.data() = a.data() * b.data(); } template <class Arithmetic> inline typename enable_if_c<std::numeric_limits<Arithmetic>::has_infinity>::type eval_divide(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) { result.data() = a.data() / b.data(); } template <class Arithmetic> inline typename disable_if_c<std::numeric_limits<Arithmetic>::has_infinity>::type eval_divide(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) { if(!b.data()) BOOST_THROW_EXCEPTION(std::overflow_error("Divide by zero")); result.data() = a.data() / b.data(); } template <class Arithmetic, class A2> inline typename enable_if<is_arithmetic<A2> >::type eval_add(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const A2& b) { result.data() = a.data() + b; } template <class Arithmetic, class A2> inline typename enable_if<is_arithmetic<A2> >::type eval_subtract(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const A2& b) { result.data() = a.data() - b; } template <class Arithmetic, class A2> inline typename enable_if<is_arithmetic<A2> >::type eval_multiply(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const A2& b) { result.data() = a.data() * b; } template <class Arithmetic, class A2> inline typename enable_if_c<(is_arithmetic<A2>::value && !std::numeric_limits<Arithmetic>::has_infinity)>::type eval_divide(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const A2& b) { if(!b) BOOST_THROW_EXCEPTION(std::overflow_error("Divide by zero")); result.data() = a.data() / b; } template <class Arithmetic, class A2> inline typename enable_if_c<(is_arithmetic<A2>::value && std::numeric_limits<Arithmetic>::has_infinity)>::type eval_divide(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const A2& b) { result.data() = a.data() / b; } template <class Arithmetic> inline bool eval_is_zero(const arithmetic_backend<Arithmetic>& val) { return val.data() == 0; } template <class Arithmetic> inline typename enable_if_c< (!std::numeric_limits<Arithmetic>::is_specialized || std::numeric_limits<Arithmetic>::is_signed), int>::type eval_get_sign(const arithmetic_backend<Arithmetic>& val) { return val.data() == 0 ? 0 : val.data() < 0 ? -1 : 1; } template <class Arithmetic> inline typename disable_if_c< (std::numeric_limits<Arithmetic>::is_specialized || std::numeric_limits<Arithmetic>::is_signed), int>::type eval_get_sign(const arithmetic_backend<Arithmetic>& val) { return val.data() == 0 ? 0 : 1; } template <class T> inline typename enable_if<is_unsigned<T>, T>::type abs(T v) { return v; } template <class Arithmetic> inline void eval_abs(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { using std::abs; using boost::multiprecision::backends::abs; result.data() = abs(o.data()); } template <class Arithmetic> inline void eval_fabs(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { result.data() = std::abs(o.data()); } template <class Arithmetic> inline void eval_floor(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = floor(o.data()); } template <class Arithmetic> inline void eval_ceil(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = ceil(o.data()); } template <class Arithmetic> inline void eval_sqrt(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = sqrt(o.data()); } template <class Arithmetic> inline int eval_fpclassify(const arithmetic_backend<Arithmetic>& o) { return (boost::math::fpclassify)(o.data()); } template <class Arithmetic> inline void eval_trunc(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = trunc(o.data()); } template <class Arithmetic> inline void eval_round(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = round(o.data()); } template <class Arithmetic> inline void eval_frexp(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, int* v) { BOOST_MATH_STD_USING result.data() = frexp(a.data(), v); } template <class Arithmetic> inline void eval_ldexp(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, int v) { BOOST_MATH_STD_USING result.data() = ldexp(a.data(), v); } template <class Arithmetic> inline void eval_exp(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = exp(o.data()); } template <class Arithmetic> inline void eval_log(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = log(o.data()); } template <class Arithmetic> inline void eval_log10(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = log10(o.data()); } template <class Arithmetic> inline void eval_sin(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = sin(o.data()); } template <class Arithmetic> inline void eval_cos(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = cos(o.data()); } template <class Arithmetic> inline void eval_tan(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = tan(o.data()); } template <class Arithmetic> inline void eval_acos(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = acos(o.data()); } template <class Arithmetic> inline void eval_asin(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = asin(o.data()); } template <class Arithmetic> inline void eval_atan(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = atan(o.data()); } template <class Arithmetic> inline void eval_sinh(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = sinh(o.data()); } template <class Arithmetic> inline void eval_cosh(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = cosh(o.data()); } template <class Arithmetic> inline void eval_tanh(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& o) { BOOST_MATH_STD_USING result.data() = tanh(o.data()); } template <class Arithmetic> inline void eval_fmod(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) { BOOST_MATH_STD_USING result.data() = fmod(a.data(), b.data()); } template <class Arithmetic> inline void eval_pow(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) { BOOST_MATH_STD_USING result.data() = pow(a.data(), b.data()); } template <class Arithmetic> inline void eval_atan2(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) { BOOST_MATH_STD_USING result.data() = atan2(a.data(), b.data()); } template <class Arithmetic, class I> inline void eval_left_shift(arithmetic_backend<Arithmetic>& result, I val) { result.data() <<= val; } template <class Arithmetic, class I> inline void eval_right_shift(arithmetic_backend<Arithmetic>& result, I val) { result.data() >>= val; } template <class Arithmetic> inline void eval_modulus(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a) { result.data() %= a.data(); } template <class Arithmetic> inline void eval_bitwise_and(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a) { result.data() &= a.data(); } template <class Arithmetic> inline void eval_bitwise_or(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a) { result.data() |= a.data(); } template <class Arithmetic> inline void eval_bitwise_xor(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a) { result.data() ^= a.data(); } template <class Arithmetic> inline void eval_complement(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a) { result.data() = ~a.data(); } template <class Arithmetic> inline void eval_gcd(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) { result.data() = boost::math::gcd(a.data(), b.data()); } template <class Arithmetic> inline void eval_lcm(arithmetic_backend<Arithmetic>& result, const arithmetic_backend<Arithmetic>& a, const arithmetic_backend<Arithmetic>& b) { result.data() = boost::math::lcm(a.data(), b.data()); } #ifdef BOOST_MSVC # pragma warning(pop) #endif } // namespace backends using boost::multiprecision::backends::arithmetic_backend; template <class Arithmetic> struct number_category<arithmetic_backend<Arithmetic> > : public mpl::int_<is_integral<Arithmetic>::value ? number_kind_integer : number_kind_floating_point>{}; namespace detail{ template <class Backend> struct double_precision_type; template<class Arithmetic, boost::multiprecision::expression_template_option ET> struct double_precision_type<number<arithmetic_backend<Arithmetic>, ET> > { typedef number<arithmetic_backend<typename double_precision_type<Arithmetic>::type>, ET> type; }; template<> struct double_precision_type<arithmetic_backend<boost::int32_t> > { typedef arithmetic_backend<boost::int64_t> type; }; } }} // namespaces #if !(defined(__SGI_STL_PORT) || defined(BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS)) // // We shouldn't need these to get code to compile, however for the sake of // "level playing field" performance comparisons they avoid the very slow // lexical_cast's that would otherwise take place. Definition has to be guarded // by the inverse of pp-logic in real_concept.hpp which defines these as a workaround // for STLPort plus some other old/broken standartd libraries. // namespace boost{ namespace math{ namespace tools{ template <> inline unsigned int real_cast<unsigned int, concepts::real_concept>(concepts::real_concept r) { return static_cast<unsigned int>(r.value()); } template <> inline int real_cast<int, concepts::real_concept>(concepts::real_concept r) { return static_cast<int>(r.value()); } template <> inline long real_cast<long, concepts::real_concept>(concepts::real_concept r) { return static_cast<long>(r.value()); } // Converts from T to narrower floating-point types, float, double & long double. template <> inline float real_cast<float, concepts::real_concept>(concepts::real_concept r) { return static_cast<float>(r.value()); } template <> inline double real_cast<double, concepts::real_concept>(concepts::real_concept r) { return static_cast<double>(r.value()); } template <> inline long double real_cast<long double, concepts::real_concept>(concepts::real_concept r) { return r.value(); } }}} #endif namespace std{ template <class Arithmetic, boost::multiprecision::expression_template_option ExpressionTemplates> class numeric_limits<boost::multiprecision::number<boost::multiprecision::arithmetic_backend<Arithmetic>, ExpressionTemplates > > : public std::numeric_limits<Arithmetic> { typedef std::numeric_limits<Arithmetic> base_type; typedef boost::multiprecision::number<boost::multiprecision::arithmetic_backend<Arithmetic>, ExpressionTemplates> number_type; public: BOOST_STATIC_CONSTEXPR number_type (min)() BOOST_NOEXCEPT { return (base_type::min)(); } BOOST_STATIC_CONSTEXPR number_type (max)() BOOST_NOEXCEPT { return (base_type::max)(); } BOOST_STATIC_CONSTEXPR number_type lowest() BOOST_NOEXCEPT { return -(max)(); } BOOST_STATIC_CONSTEXPR number_type epsilon() BOOST_NOEXCEPT { return base_type::epsilon(); } BOOST_STATIC_CONSTEXPR number_type round_error() BOOST_NOEXCEPT { return epsilon() / 2; } BOOST_STATIC_CONSTEXPR number_type infinity() BOOST_NOEXCEPT { return base_type::infinity(); } BOOST_STATIC_CONSTEXPR number_type quiet_NaN() BOOST_NOEXCEPT { return base_type::quiet_NaN(); } BOOST_STATIC_CONSTEXPR number_type signaling_NaN() BOOST_NOEXCEPT { return base_type::signaling_NaN(); } BOOST_STATIC_CONSTEXPR number_type denorm_min() BOOST_NOEXCEPT { return base_type::denorm_min(); } }; template<> class numeric_limits<boost::math::concepts::real_concept> : public std::numeric_limits<long double> { typedef std::numeric_limits<long double> base_type; typedef boost::math::concepts::real_concept number_type; public: static const number_type (min)() BOOST_NOEXCEPT { return (base_type::min)(); } static const number_type (max)() BOOST_NOEXCEPT { return (base_type::max)(); } static const number_type lowest() BOOST_NOEXCEPT { return -(max)(); } static const number_type epsilon() BOOST_NOEXCEPT { return base_type::epsilon(); } static const number_type round_error() BOOST_NOEXCEPT { return epsilon() / 2; } static const number_type infinity() BOOST_NOEXCEPT { return base_type::infinity(); } static const number_type quiet_NaN() BOOST_NOEXCEPT { return base_type::quiet_NaN(); } static const number_type signaling_NaN() BOOST_NOEXCEPT { return base_type::signaling_NaN(); } static const number_type denorm_min() BOOST_NOEXCEPT { return base_type::denorm_min(); } }; } #include <boost/multiprecision/detail/integer_ops.hpp> #endif