boost/multiprecision/cpp_dec_float.hpp
/////////////////////////////////////////////////////////////////////////////// // Copyright Christopher Kormanyos 2002 - 2013. // Copyright 2011 -2013 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) // // This work is based on an earlier work: // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 // // Note that there are no "noexcept" specifications on the functions in this file: there are too many // calls to lexical_cast (and similar) to easily analyse the code for correctness. So until compilers // can detect noexcept misuse at compile time, the only realistic option is to simply not use it here. // #ifndef BOOST_MP_CPP_DEC_FLOAT_BACKEND_HPP #define BOOST_MP_CPP_DEC_FLOAT_BACKEND_HPP #include <boost/config.hpp> #include <boost/cstdint.hpp> #include <limits> #ifndef BOOST_NO_CXX11_HDR_ARRAY #include <array> #else #include <boost/array.hpp> #endif #include <boost/cstdint.hpp> #include <boost/functional/hash_fwd.hpp> #include <boost/multiprecision/number.hpp> #include <boost/multiprecision/detail/big_lanczos.hpp> #include <boost/multiprecision/detail/dynamic_array.hpp> // // Headers required for Boost.Math integration: // #include <boost/math/policies/policy.hpp> // // Some includes we need from Boost.Math, since we rely on that library to provide these functions: // #include <boost/math/special_functions/asinh.hpp> #include <boost/math/special_functions/acosh.hpp> #include <boost/math/special_functions/atanh.hpp> #include <boost/math/special_functions/cbrt.hpp> #include <boost/math/special_functions/expm1.hpp> #include <boost/math/special_functions/gamma.hpp> #ifdef BOOST_MSVC #pragma warning(push) #pragma warning(disable : 6326) // comparison of two constants #endif namespace boost { namespace multiprecision { namespace backends { template <unsigned Digits10, class ExponentType = boost::int32_t, class Allocator = void> class cpp_dec_float; } // namespace backends template <unsigned Digits10, class ExponentType, class Allocator> struct number_category<backends::cpp_dec_float<Digits10, ExponentType, Allocator> > : public mpl::int_<number_kind_floating_point> {}; namespace backends { template <unsigned Digits10, class ExponentType, class Allocator> class cpp_dec_float { private: static const boost::int32_t cpp_dec_float_digits10_setting = Digits10; // We need at least 16-bits in the exponent type to do anything sensible: BOOST_STATIC_ASSERT_MSG(boost::is_signed<ExponentType>::value, "ExponentType must be a signed built in integer type."); BOOST_STATIC_ASSERT_MSG(sizeof(ExponentType) > 1, "ExponentType is too small."); public: typedef mpl::list<boost::long_long_type> signed_types; typedef mpl::list<boost::ulong_long_type> unsigned_types; typedef mpl::list<long double> float_types; typedef ExponentType exponent_type; static const boost::int32_t cpp_dec_float_radix = 10L; static const boost::int32_t cpp_dec_float_digits10_limit_lo = 9L; static const boost::int32_t cpp_dec_float_digits10_limit_hi = boost::integer_traits<boost::int32_t>::const_max - 100; static const boost::int32_t cpp_dec_float_digits10 = ((cpp_dec_float_digits10_setting < cpp_dec_float_digits10_limit_lo) ? cpp_dec_float_digits10_limit_lo : ((cpp_dec_float_digits10_setting > cpp_dec_float_digits10_limit_hi) ? cpp_dec_float_digits10_limit_hi : cpp_dec_float_digits10_setting)); static const ExponentType cpp_dec_float_max_exp10 = (static_cast<ExponentType>(1) << (std::numeric_limits<ExponentType>::digits - 5)); static const ExponentType cpp_dec_float_min_exp10 = -cpp_dec_float_max_exp10; static const ExponentType cpp_dec_float_max_exp = cpp_dec_float_max_exp10; static const ExponentType cpp_dec_float_min_exp = cpp_dec_float_min_exp10; BOOST_STATIC_ASSERT((cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10 == -cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10)); private: static const boost::int32_t cpp_dec_float_elem_digits10 = 8L; static const boost::int32_t cpp_dec_float_elem_mask = 100000000L; BOOST_STATIC_ASSERT(0 == cpp_dec_float_max_exp10 % cpp_dec_float_elem_digits10); // There are three guard limbs. // 1) The first limb has 'play' from 1...8 decimal digits. // 2) The last limb also has 'play' from 1...8 decimal digits. // 3) One limb can get lost when justifying after multiply, // as only half of the triangle is multiplied and a carry // from below is missing. static const boost::int32_t cpp_dec_float_elem_number_request = static_cast<boost::int32_t>((cpp_dec_float_digits10 / cpp_dec_float_elem_digits10) + (((cpp_dec_float_digits10 % cpp_dec_float_elem_digits10) != 0) ? 1 : 0)); // The number of elements needed (with a minimum of two) plus three added guard limbs. static const boost::int32_t cpp_dec_float_elem_number = static_cast<boost::int32_t>(((cpp_dec_float_elem_number_request < 2L) ? 2L : cpp_dec_float_elem_number_request) + 3L); public: static const boost::int32_t cpp_dec_float_total_digits10 = static_cast<boost::int32_t>(cpp_dec_float_elem_number * cpp_dec_float_elem_digits10); private: typedef enum enum_fpclass_type { cpp_dec_float_finite, cpp_dec_float_inf, cpp_dec_float_NaN } fpclass_type; #ifndef BOOST_NO_CXX11_HDR_ARRAY typedef typename mpl::if_<is_void<Allocator>, std::array<boost::uint32_t, cpp_dec_float_elem_number>, detail::dynamic_array<boost::uint32_t, cpp_dec_float_elem_number, Allocator> >::type array_type; #else typedef typename mpl::if_<is_void<Allocator>, boost::array<boost::uint32_t, cpp_dec_float_elem_number>, detail::dynamic_array<boost::uint32_t, cpp_dec_float_elem_number, Allocator> >::type array_type; #endif array_type data; ExponentType exp; bool neg; fpclass_type fpclass; boost::int32_t prec_elem; // // Special values constructor: // cpp_dec_float(fpclass_type c) : data(), exp(static_cast<ExponentType>(0)), neg(false), fpclass(c), prec_elem(cpp_dec_float_elem_number) {} // // Static data initializer: // struct initializer { initializer() { cpp_dec_float<Digits10, ExponentType, Allocator>::nan(); cpp_dec_float<Digits10, ExponentType, Allocator>::inf(); (cpp_dec_float<Digits10, ExponentType, Allocator>::min)(); (cpp_dec_float<Digits10, ExponentType, Allocator>::max)(); cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); cpp_dec_float<Digits10, ExponentType, Allocator>::one(); cpp_dec_float<Digits10, ExponentType, Allocator>::two(); cpp_dec_float<Digits10, ExponentType, Allocator>::half(); cpp_dec_float<Digits10, ExponentType, Allocator>::double_min(); cpp_dec_float<Digits10, ExponentType, Allocator>::double_max(); cpp_dec_float<Digits10, ExponentType, Allocator>::long_double_max(); cpp_dec_float<Digits10, ExponentType, Allocator>::long_double_min(); cpp_dec_float<Digits10, ExponentType, Allocator>::long_long_max(); cpp_dec_float<Digits10, ExponentType, Allocator>::long_long_min(); cpp_dec_float<Digits10, ExponentType, Allocator>::ulong_long_max(); cpp_dec_float<Digits10, ExponentType, Allocator>::eps(); cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(0); } void do_nothing() {} }; static initializer init; public: // Constructors cpp_dec_float() BOOST_MP_NOEXCEPT_IF(noexcept(array_type())) : data(), exp(static_cast<ExponentType>(0)), neg(false), fpclass(cpp_dec_float_finite), prec_elem(cpp_dec_float_elem_number) {} cpp_dec_float(const char* s) : data(), exp(static_cast<ExponentType>(0)), neg(false), fpclass(cpp_dec_float_finite), prec_elem(cpp_dec_float_elem_number) { *this = s; } template <class I> cpp_dec_float(I i, typename enable_if<is_unsigned<I> >::type* = 0) : data(), exp(static_cast<ExponentType>(0)), neg(false), fpclass(cpp_dec_float_finite), prec_elem(cpp_dec_float_elem_number) { from_unsigned_long_long(i); } template <class I> cpp_dec_float(I i, typename enable_if<is_signed<I> >::type* = 0) : data(), exp(static_cast<ExponentType>(0)), neg(false), fpclass(cpp_dec_float_finite), prec_elem(cpp_dec_float_elem_number) { if (i < 0) { from_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(i)); negate(); } else from_unsigned_long_long(i); } cpp_dec_float(const cpp_dec_float& f) BOOST_MP_NOEXCEPT_IF(noexcept(array_type(std::declval<const array_type&>()))) : data(f.data), exp(f.exp), neg(f.neg), fpclass(f.fpclass), prec_elem(f.prec_elem) {} template <unsigned D, class ET, class A> cpp_dec_float(const cpp_dec_float<D, ET, A>& f, typename enable_if_c<D <= Digits10>::type* = 0) : data(), exp(f.exp), neg(f.neg), fpclass(static_cast<fpclass_type>(static_cast<int>(f.fpclass))), prec_elem(cpp_dec_float_elem_number) { std::copy(f.data.begin(), f.data.begin() + f.prec_elem, data.begin()); } template <unsigned D, class ET, class A> explicit cpp_dec_float(const cpp_dec_float<D, ET, A>& f, typename disable_if_c<D <= Digits10>::type* = 0) : data(), exp(f.exp), neg(f.neg), fpclass(static_cast<fpclass_type>(static_cast<int>(f.fpclass))), prec_elem(cpp_dec_float_elem_number) { // TODO: this doesn't round! std::copy(f.data.begin(), f.data.begin() + prec_elem, data.begin()); } template <class F> cpp_dec_float(const F val, typename enable_if_c<is_floating_point<F>::value #ifdef BOOST_HAS_FLOAT128 && !boost::is_same<F, __float128>::value #endif >::type* = 0) : data(), exp(static_cast<ExponentType>(0)), neg(false), fpclass(cpp_dec_float_finite), prec_elem(cpp_dec_float_elem_number) { *this = val; } cpp_dec_float(const double mantissa, const ExponentType exponent); std::size_t hash() const { std::size_t result = 0; for (int i = 0; i < prec_elem; ++i) boost::hash_combine(result, data[i]); boost::hash_combine(result, exp); boost::hash_combine(result, neg); boost::hash_combine(result, fpclass); return result; } // Specific special values. static const cpp_dec_float& nan() { static const cpp_dec_float val(cpp_dec_float_NaN); init.do_nothing(); return val; } static const cpp_dec_float& inf() { static const cpp_dec_float val(cpp_dec_float_inf); init.do_nothing(); return val; } static const cpp_dec_float&(max)() { init.do_nothing(); static cpp_dec_float val_max = std::string("1.0e" + boost::lexical_cast<std::string>(cpp_dec_float_max_exp10)).c_str(); return val_max; } static const cpp_dec_float&(min)() { init.do_nothing(); static cpp_dec_float val_min = std::string("1.0e" + boost::lexical_cast<std::string>(cpp_dec_float_min_exp10)).c_str(); return val_min; } static const cpp_dec_float& zero() { init.do_nothing(); static cpp_dec_float val(static_cast<boost::ulong_long_type>(0u)); return val; } static const cpp_dec_float& one() { init.do_nothing(); static cpp_dec_float val(static_cast<boost::ulong_long_type>(1u)); return val; } static const cpp_dec_float& two() { init.do_nothing(); static cpp_dec_float val(static_cast<boost::ulong_long_type>(2u)); return val; } static const cpp_dec_float& half() { init.do_nothing(); static cpp_dec_float val(0.5L); return val; } static const cpp_dec_float& double_min() { init.do_nothing(); static cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::min)())); return val; } static const cpp_dec_float& double_max() { init.do_nothing(); static cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::max)())); return val; } static const cpp_dec_float& long_double_min() { init.do_nothing(); #ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS static cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::min)())); #else static cpp_dec_float val((std::numeric_limits<long double>::min)()); #endif return val; } static const cpp_dec_float& long_double_max() { init.do_nothing(); #ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS static cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::max)())); #else static cpp_dec_float val((std::numeric_limits<long double>::max)()); #endif return val; } static const cpp_dec_float& long_long_max() { init.do_nothing(); static cpp_dec_float val((std::numeric_limits<boost::long_long_type>::max)()); return val; } static const cpp_dec_float& long_long_min() { init.do_nothing(); static cpp_dec_float val((std::numeric_limits<boost::long_long_type>::min)()); return val; } static const cpp_dec_float& ulong_long_max() { init.do_nothing(); static cpp_dec_float val((std::numeric_limits<boost::ulong_long_type>::max)()); return val; } static const cpp_dec_float& eps() { init.do_nothing(); static cpp_dec_float val(1.0, 1 - static_cast<int>(cpp_dec_float_digits10)); return val; } // Basic operations. cpp_dec_float& operator=(const cpp_dec_float& v) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<array_type&>() = std::declval<const array_type&>())) { data = v.data; exp = v.exp; neg = v.neg; fpclass = v.fpclass; prec_elem = v.prec_elem; return *this; } template <unsigned D> cpp_dec_float& operator=(const cpp_dec_float<D>& f) { exp = f.exp; neg = f.neg; fpclass = static_cast<enum_fpclass_type>(static_cast<int>(f.fpclass)); unsigned elems = (std::min)(f.prec_elem, cpp_dec_float_elem_number); std::copy(f.data.begin(), f.data.begin() + elems, data.begin()); std::fill(data.begin() + elems, data.end(), 0); prec_elem = cpp_dec_float_elem_number; return *this; } cpp_dec_float& operator=(boost::long_long_type v) { if (v < 0) { from_unsigned_long_long(1u - boost::ulong_long_type(v + 1)); // Avoid undefined behaviour in negation of minimum value for long long negate(); } else from_unsigned_long_long(v); return *this; } cpp_dec_float& operator=(boost::ulong_long_type v) { from_unsigned_long_long(v); return *this; } cpp_dec_float& operator=(long double v); cpp_dec_float& operator=(const char* v) { rd_string(v); return *this; } cpp_dec_float& operator+=(const cpp_dec_float& v); cpp_dec_float& operator-=(const cpp_dec_float& v); cpp_dec_float& operator*=(const cpp_dec_float& v); cpp_dec_float& operator/=(const cpp_dec_float& v); cpp_dec_float& add_unsigned_long_long(const boost::ulong_long_type n) { cpp_dec_float t; t.from_unsigned_long_long(n); return *this += t; } cpp_dec_float& sub_unsigned_long_long(const boost::ulong_long_type n) { cpp_dec_float t; t.from_unsigned_long_long(n); return *this -= t; } cpp_dec_float& mul_unsigned_long_long(const boost::ulong_long_type n); cpp_dec_float& div_unsigned_long_long(const boost::ulong_long_type n); // Elementary primitives. cpp_dec_float& calculate_inv(); cpp_dec_float& calculate_sqrt(); void negate() { if (!iszero()) neg = !neg; } // Comparison functions bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_NaN); } bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_inf); } bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_finite); } bool iszero() const { return ((fpclass == cpp_dec_float_finite) && (data[0u] == 0u)); } bool isone() const; bool isint() const; bool isneg() const { return neg; } // Operators pre-increment and pre-decrement cpp_dec_float& operator++() { return *this += one(); } cpp_dec_float& operator--() { return *this -= one(); } std::string str(boost::intmax_t digits, std::ios_base::fmtflags f) const; int compare(const cpp_dec_float& v) const; template <class V> int compare(const V& v) const { cpp_dec_float<Digits10, ExponentType, Allocator> t; t = v; return compare(t); } void swap(cpp_dec_float& v) { data.swap(v.data); std::swap(exp, v.exp); std::swap(neg, v.neg); std::swap(fpclass, v.fpclass); std::swap(prec_elem, v.prec_elem); } double extract_double() const; long double extract_long_double() const; boost::long_long_type extract_signed_long_long() const; boost::ulong_long_type extract_unsigned_long_long() const; void extract_parts(double& mantissa, ExponentType& exponent) const; cpp_dec_float extract_integer_part() const; void precision(const boost::int32_t prec_digits) { if (prec_digits >= cpp_dec_float_total_digits10) { prec_elem = cpp_dec_float_elem_number; } else { const boost::int32_t elems = static_cast<boost::int32_t>(static_cast<boost::int32_t>((prec_digits + (cpp_dec_float_elem_digits10 / 2)) / cpp_dec_float_elem_digits10) + static_cast<boost::int32_t>(((prec_digits % cpp_dec_float_elem_digits10) != 0) ? 1 : 0)); prec_elem = (std::min)(cpp_dec_float_elem_number, (std::max)(elems, static_cast<boost::int32_t>(2))); } } static cpp_dec_float pow2(boost::long_long_type i); ExponentType order() const { const bool bo_order_is_zero = ((!(isfinite)()) || (data[0] == static_cast<boost::uint32_t>(0u))); // // Binary search to find the order of the leading term: // ExponentType prefix = 0; if (data[0] >= 100000UL) { if (data[0] >= 10000000UL) { if (data[0] >= 100000000UL) { if (data[0] >= 1000000000UL) prefix = 9; else prefix = 8; } else prefix = 7; } else { if (data[0] >= 1000000UL) prefix = 6; else prefix = 5; } } else { if (data[0] >= 1000UL) { if (data[0] >= 10000UL) prefix = 4; else prefix = 3; } else { if (data[0] >= 100) prefix = 2; else if (data[0] >= 10) prefix = 1; } } return (bo_order_is_zero ? static_cast<ExponentType>(0) : static_cast<ExponentType>(exp + prefix)); } template <class Archive> void serialize(Archive& ar, const unsigned int /*version*/) { for (unsigned i = 0; i < data.size(); ++i) ar& boost::make_nvp("digit", data[i]); ar& boost::make_nvp("exponent", exp); ar& boost::make_nvp("sign", neg); ar& boost::make_nvp("class-type", fpclass); ar& boost::make_nvp("precision", prec_elem); } private: static bool data_elem_is_non_zero_predicate(const boost::uint32_t& d) { return (d != static_cast<boost::uint32_t>(0u)); } static bool data_elem_is_non_nine_predicate(const boost::uint32_t& d) { return (d != static_cast<boost::uint32_t>(cpp_dec_float::cpp_dec_float_elem_mask - 1)); } static bool char_is_nonzero_predicate(const char& c) { return (c != static_cast<char>('0')); } void from_unsigned_long_long(const boost::ulong_long_type u); int cmp_data(const array_type& vd) const; static boost::uint32_t mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p); static boost::uint32_t mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); static boost::uint32_t div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); bool rd_string(const char* const s); template <unsigned D, class ET, class A> friend class cpp_dec_float; }; template <unsigned Digits10, class ExponentType, class Allocator> typename cpp_dec_float<Digits10, ExponentType, Allocator>::initializer cpp_dec_float<Digits10, ExponentType, Allocator>::init; template <unsigned Digits10, class ExponentType, class Allocator> const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_radix; template <unsigned Digits10, class ExponentType, class Allocator> const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_setting; template <unsigned Digits10, class ExponentType, class Allocator> const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_limit_lo; template <unsigned Digits10, class ExponentType, class Allocator> const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_limit_hi; template <unsigned Digits10, class ExponentType, class Allocator> const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10; template <unsigned Digits10, class ExponentType, class Allocator> const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp; template <unsigned Digits10, class ExponentType, class Allocator> const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp; template <unsigned Digits10, class ExponentType, class Allocator> const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10; template <unsigned Digits10, class ExponentType, class Allocator> const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10; template <unsigned Digits10, class ExponentType, class Allocator> const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_digits10; template <unsigned Digits10, class ExponentType, class Allocator> const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_number_request; template <unsigned Digits10, class ExponentType, class Allocator> const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_number; template <unsigned Digits10, class ExponentType, class Allocator> const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_mask; template <unsigned Digits10, class ExponentType, class Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator+=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v) { if ((isnan)()) { return *this; } if ((isinf)()) { if ((v.isinf)() && (isneg() != v.isneg())) { *this = nan(); } return *this; } if (iszero()) { return operator=(v); } if ((v.isnan)() || (v.isinf)()) { *this = v; return *this; } // Get the offset for the add/sub operation. static const ExponentType max_delta_exp = static_cast<ExponentType>((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10); const ExponentType ofs_exp = static_cast<ExponentType>(exp - v.exp); // Check if the operation is out of range, requiring special handling. if (v.iszero() || (ofs_exp > max_delta_exp)) { // Result is *this unchanged since v is negligible compared to *this. return *this; } else if (ofs_exp < -max_delta_exp) { // Result is *this = v since *this is negligible compared to v. return operator=(v); } // Do the add/sub operation. typename array_type::iterator p_u = data.begin(); typename array_type::const_iterator p_v = v.data.begin(); bool b_copy = false; const boost::int32_t ofs = static_cast<boost::int32_t>(static_cast<boost::int32_t>(ofs_exp) / cpp_dec_float_elem_digits10); array_type n_data; if (neg == v.neg) { // Add v to *this, where the data array of either *this or v // might have to be treated with a positive, negative or zero offset. // The result is stored in *this. The data are added one element // at a time, each element with carry. if (ofs >= static_cast<boost::int32_t>(0)) { std::copy(v.data.begin(), v.data.end() - static_cast<size_t>(ofs), n_data.begin() + static_cast<size_t>(ofs)); std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(ofs), static_cast<boost::uint32_t>(0u)); p_v = n_data.begin(); } else { std::copy(data.begin(), data.end() - static_cast<size_t>(-ofs), n_data.begin() + static_cast<size_t>(-ofs)); std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(-ofs), static_cast<boost::uint32_t>(0u)); p_u = n_data.begin(); b_copy = true; } // Addition algorithm boost::uint32_t carry = static_cast<boost::uint32_t>(0u); for (boost::int32_t j = static_cast<boost::int32_t>(cpp_dec_float_elem_number - static_cast<boost::int32_t>(1)); j >= static_cast<boost::int32_t>(0); j--) { boost::uint32_t t = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(p_u[j] + p_v[j]) + carry); carry = t / static_cast<boost::uint32_t>(cpp_dec_float_elem_mask); p_u[j] = static_cast<boost::uint32_t>(t - static_cast<boost::uint32_t>(carry * static_cast<boost::uint32_t>(cpp_dec_float_elem_mask))); } if (b_copy) { data = n_data; exp = v.exp; } // There needs to be a carry into the element -1 of the array data if (carry != static_cast<boost::uint32_t>(0u)) { std::copy_backward(data.begin(), data.end() - static_cast<std::size_t>(1u), data.end()); data[0] = carry; exp += static_cast<ExponentType>(cpp_dec_float_elem_digits10); } } else { // Subtract v from *this, where the data array of either *this or v // might have to be treated with a positive, negative or zero offset. if ((ofs > static_cast<boost::int32_t>(0)) || ((ofs == static_cast<boost::int32_t>(0)) && (cmp_data(v.data) > static_cast<boost::int32_t>(0)))) { // In this case, |u| > |v| and ofs is positive. // Copy the data of v, shifted down to a lower value // into the data array m_n. Set the operand pointer p_v // to point to the copied, shifted data m_n. std::copy(v.data.begin(), v.data.end() - static_cast<size_t>(ofs), n_data.begin() + static_cast<size_t>(ofs)); std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(ofs), static_cast<boost::uint32_t>(0u)); p_v = n_data.begin(); } else { if (ofs != static_cast<boost::int32_t>(0)) { // In this case, |u| < |v| and ofs is negative. // Shift the data of u down to a lower value. std::copy_backward(data.begin(), data.end() - static_cast<size_t>(-ofs), data.end()); std::fill(data.begin(), data.begin() + static_cast<size_t>(-ofs), static_cast<boost::uint32_t>(0u)); } // Copy the data of v into the data array n_data. // Set the u-pointer p_u to point to m_n and the // operand pointer p_v to point to the shifted // data m_data. n_data = v.data; p_u = n_data.begin(); p_v = data.begin(); b_copy = true; } boost::int32_t j; // Subtraction algorithm boost::int32_t borrow = static_cast<boost::int32_t>(0); for (j = static_cast<boost::int32_t>(cpp_dec_float_elem_number - static_cast<boost::int32_t>(1)); j >= static_cast<boost::int32_t>(0); j--) { boost::int32_t t = static_cast<boost::int32_t>(static_cast<boost::int32_t>(static_cast<boost::int32_t>(p_u[j]) - static_cast<boost::int32_t>(p_v[j])) - borrow); // Underflow? Borrow? if (t < static_cast<boost::int32_t>(0)) { // Yes, underflow and borrow t += static_cast<boost::int32_t>(cpp_dec_float_elem_mask); borrow = static_cast<boost::int32_t>(1); } else { borrow = static_cast<boost::int32_t>(0); } p_u[j] = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(t) % static_cast<boost::uint32_t>(cpp_dec_float_elem_mask)); } if (b_copy) { data = n_data; exp = v.exp; neg = v.neg; } // Is it necessary to justify the data? const typename array_type::const_iterator first_nonzero_elem = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate); if (first_nonzero_elem != data.begin()) { if (first_nonzero_elem == data.end()) { // This result of the subtraction is exactly zero. // Reset the sign and the exponent. neg = false; exp = static_cast<ExponentType>(0); } else { // Justify the data const std::size_t sj = static_cast<std::size_t>(std::distance<typename array_type::const_iterator>(data.begin(), first_nonzero_elem)); std::copy(data.begin() + static_cast<std::size_t>(sj), data.end(), data.begin()); std::fill(data.end() - sj, data.end(), static_cast<boost::uint32_t>(0u)); exp -= static_cast<ExponentType>(sj * static_cast<std::size_t>(cpp_dec_float_elem_digits10)); } } } // Handle underflow. if (iszero()) return (*this = zero()); // Check for potential overflow. const bool b_result_might_overflow = (exp >= static_cast<ExponentType>(cpp_dec_float_max_exp10)); // Handle overflow. if (b_result_might_overflow) { const bool b_result_is_neg = neg; neg = false; if (compare((cpp_dec_float::max)()) > 0) *this = inf(); neg = b_result_is_neg; } return *this; } template <unsigned Digits10, class ExponentType, class Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator-=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v) { // Use *this - v = -(-*this + v). negate(); *this += v; negate(); return *this; } template <unsigned Digits10, class ExponentType, class Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator*=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v) { // Evaluate the sign of the result. const bool b_result_is_neg = (neg != v.neg); // Artificially set the sign of the result to be positive. neg = false; // Handle special cases like zero, inf and NaN. const bool b_u_is_inf = (isinf)(); const bool b_v_is_inf = (v.isinf)(); const bool b_u_is_zero = iszero(); const bool b_v_is_zero = v.iszero(); if (((isnan)() || (v.isnan)()) || (b_u_is_inf && b_v_is_zero) || (b_v_is_inf && b_u_is_zero)) { *this = nan(); return *this; } if (b_u_is_inf || b_v_is_inf) { *this = inf(); if (b_result_is_neg) negate(); return *this; } if (b_u_is_zero || b_v_is_zero) { return *this = zero(); } // Check for potential overflow or underflow. const bool b_result_might_overflow = ((exp + v.exp) >= static_cast<ExponentType>(cpp_dec_float_max_exp10)); const bool b_result_might_underflow = ((exp + v.exp) <= static_cast<ExponentType>(cpp_dec_float_min_exp10)); // Set the exponent of the result. exp += v.exp; const boost::int32_t prec_mul = (std::min)(prec_elem, v.prec_elem); const boost::uint32_t carry = mul_loop_uv(data.data(), v.data.data(), prec_mul); // Handle a potential carry. if (carry != static_cast<boost::uint32_t>(0u)) { exp += cpp_dec_float_elem_digits10; // Shift the result of the multiplication one element to the right... std::copy_backward(data.begin(), data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)), data.begin() + static_cast<std::size_t>(prec_elem)); // ... And insert the carry. data.front() = carry; } // Handle overflow. if (b_result_might_overflow && (compare((cpp_dec_float::max)()) > 0)) { *this = inf(); } // Handle underflow. if (b_result_might_underflow && (compare((cpp_dec_float::min)()) < 0)) { *this = zero(); return *this; } // Set the sign of the result. neg = b_result_is_neg; return *this; } template <unsigned Digits10, class ExponentType, class Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator/=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v) { if (iszero()) { if ((v.isnan)()) { return *this = v; } else if (v.iszero()) { return *this = nan(); } } const bool u_and_v_are_finite_and_identical = ((isfinite)() && (fpclass == v.fpclass) && (exp == v.exp) && (cmp_data(v.data) == static_cast<boost::int32_t>(0))); if (u_and_v_are_finite_and_identical) { if (neg != v.neg) { *this = one(); negate(); } else *this = one(); return *this; } else { cpp_dec_float t(v); t.calculate_inv(); return operator*=(t); } } template <unsigned Digits10, class ExponentType, class Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::mul_unsigned_long_long(const boost::ulong_long_type n) { // Multiply *this with a constant boost::ulong_long_type. // Evaluate the sign of the result. const bool b_neg = neg; // Artificially set the sign of the result to be positive. neg = false; // Handle special cases like zero, inf and NaN. const bool b_u_is_inf = (isinf)(); const bool b_n_is_zero = (n == static_cast<boost::int32_t>(0)); if ((isnan)() || (b_u_is_inf && b_n_is_zero)) { return (*this = nan()); } if (b_u_is_inf) { *this = inf(); if (b_neg) negate(); return *this; } if (iszero() || b_n_is_zero) { // Multiplication by zero. return *this = zero(); } if (n >= static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask)) { neg = b_neg; cpp_dec_float t; t = n; return operator*=(t); } if (n == static_cast<boost::ulong_long_type>(1u)) { neg = b_neg; return *this; } // Set up the multiplication loop. const boost::uint32_t nn = static_cast<boost::uint32_t>(n); const boost::uint32_t carry = mul_loop_n(data.data(), nn, prec_elem); // Handle the carry and adjust the exponent. if (carry != static_cast<boost::uint32_t>(0u)) { exp += static_cast<ExponentType>(cpp_dec_float_elem_digits10); // Shift the result of the multiplication one element to the right. std::copy_backward(data.begin(), data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)), data.begin() + static_cast<std::size_t>(prec_elem)); data.front() = static_cast<boost::uint32_t>(carry); } // Check for potential overflow. const bool b_result_might_overflow = (exp >= cpp_dec_float_max_exp10); // Handle overflow. if (b_result_might_overflow && (compare((cpp_dec_float::max)()) > 0)) { *this = inf(); } // Set the sign. neg = b_neg; return *this; } template <unsigned Digits10, class ExponentType, class Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::div_unsigned_long_long(const boost::ulong_long_type n) { // Divide *this by a constant boost::ulong_long_type. // Evaluate the sign of the result. const bool b_neg = neg; // Artificially set the sign of the result to be positive. neg = false; // Handle special cases like zero, inf and NaN. if ((isnan)()) { return *this; } if ((isinf)()) { *this = inf(); if (b_neg) negate(); return *this; } if (n == static_cast<boost::ulong_long_type>(0u)) { // Divide by 0. if (iszero()) { *this = nan(); return *this; } else { *this = inf(); if (isneg()) negate(); return *this; } } if (iszero()) { return *this; } if (n >= static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask)) { neg = b_neg; cpp_dec_float t; t = n; return operator/=(t); } const boost::uint32_t nn = static_cast<boost::uint32_t>(n); if (nn > static_cast<boost::uint32_t>(1u)) { // Do the division loop. const boost::uint32_t prev = div_loop_n(data.data(), nn, prec_elem); // Determine if one leading zero is in the result data. if (data[0] == static_cast<boost::uint32_t>(0u)) { // Adjust the exponent exp -= static_cast<ExponentType>(cpp_dec_float_elem_digits10); // Shift result of the division one element to the left. std::copy(data.begin() + static_cast<std::size_t>(1u), data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)), data.begin()); data[prec_elem - static_cast<boost::int32_t>(1)] = static_cast<boost::uint32_t>(static_cast<boost::uint64_t>(prev * static_cast<boost::uint64_t>(cpp_dec_float_elem_mask)) / nn); } } // Check for potential underflow. const bool b_result_might_underflow = (exp <= cpp_dec_float_min_exp10); // Handle underflow. if (b_result_might_underflow && (compare((cpp_dec_float::min)()) < 0)) return (*this = zero()); // Set the sign of the result. neg = b_neg; return *this; } template <unsigned Digits10, class ExponentType, class Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::calculate_inv() { // Compute the inverse of *this. const bool b_neg = neg; neg = false; // Handle special cases like zero, inf and NaN. if (iszero()) { *this = inf(); if (b_neg) negate(); return *this; } if ((isnan)()) { return *this; } if ((isinf)()) { return *this = zero(); } if (isone()) { if (b_neg) negate(); return *this; } // Save the original *this. cpp_dec_float<Digits10, ExponentType, Allocator> x(*this); // Generate the initial estimate using division. // Extract the mantissa and exponent for a "manual" // computation of the estimate. double dd; ExponentType ne; x.extract_parts(dd, ne); // Do the inverse estimate using double precision estimates of mantissa and exponent. operator=(cpp_dec_float<Digits10, ExponentType, Allocator>(1.0 / dd, -ne)); // Compute the inverse of *this. Quadratically convergent Newton-Raphson iteration // is used. During the iterative steps, the precision of the calculation is limited // to the minimum required in order to minimize the run-time. static const boost::int32_t double_digits10_minus_a_few = std::numeric_limits<double>::digits10 - 3; for (boost::int32_t digits = double_digits10_minus_a_few; digits <= cpp_dec_float_total_digits10; digits *= static_cast<boost::int32_t>(2)) { // Adjust precision of the terms. precision(static_cast<boost::int32_t>((digits + 10) * static_cast<boost::int32_t>(2))); x.precision(static_cast<boost::int32_t>((digits + 10) * static_cast<boost::int32_t>(2))); // Next iteration. cpp_dec_float t(*this); t *= x; t -= two(); t.negate(); *this *= t; } neg = b_neg; prec_elem = cpp_dec_float_elem_number; return *this; } template <unsigned Digits10, class ExponentType, class Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::calculate_sqrt() { // Compute the square root of *this. if ((isinf)() && !isneg()) { return *this; } if (isneg() || (!(isfinite)())) { *this = nan(); errno = EDOM; return *this; } if (iszero() || isone()) { return *this; } // Save the original *this. cpp_dec_float<Digits10, ExponentType, Allocator> x(*this); // Generate the initial estimate using division. // Extract the mantissa and exponent for a "manual" // computation of the estimate. double dd; ExponentType ne; extract_parts(dd, ne); // Force the exponent to be an even multiple of two. if ((ne % static_cast<ExponentType>(2)) != static_cast<ExponentType>(0)) { ++ne; dd /= 10.0; } // Setup the iteration. // Estimate the square root using simple manipulations. const double sqd = std::sqrt(dd); *this = cpp_dec_float<Digits10, ExponentType, Allocator>(sqd, static_cast<ExponentType>(ne / static_cast<ExponentType>(2))); // Estimate 1.0 / (2.0 * x0) using simple manipulations. cpp_dec_float<Digits10, ExponentType, Allocator> vi(0.5 / sqd, static_cast<ExponentType>(-ne / static_cast<ExponentType>(2))); // Compute the square root of x. Coupled Newton iteration // as described in "Pi Unleashed" is used. During the // iterative steps, the precision of the calculation is // limited to the minimum required in order to minimize // the run-time. // // Book references: // https://doi.org/10.1007/978-3-642-56735-3 // http://www.amazon.com/exec/obidos/tg/detail/-/3540665722/qid=1035535482/sr=8-7/ref=sr_8_7/104-3357872-6059916?v=glance&n=507846 static const boost::uint32_t double_digits10_minus_a_few = std::numeric_limits<double>::digits10 - 3; for (boost::int32_t digits = double_digits10_minus_a_few; digits <= cpp_dec_float_total_digits10; digits *= 2u) { // Adjust precision of the terms. precision((digits + 10) * 2); vi.precision((digits + 10) * 2); // Next iteration of vi cpp_dec_float t(*this); t *= vi; t.negate(); t.mul_unsigned_long_long(2u); t += one(); t *= vi; vi += t; // Next iteration of *this t = *this; t *= *this; t.negate(); t += x; t *= vi; *this += t; } prec_elem = cpp_dec_float_elem_number; return *this; } template <unsigned Digits10, class ExponentType, class Allocator> int cpp_dec_float<Digits10, ExponentType, Allocator>::cmp_data(const array_type& vd) const { // Compare the data of *this with those of v. // Return +1 for *this > v // 0 for *this = v // -1 for *this < v const std::pair<typename array_type::const_iterator, typename array_type::const_iterator> mismatch_pair = std::mismatch(data.begin(), data.end(), vd.begin()); const bool is_equal = ((mismatch_pair.first == data.end()) && (mismatch_pair.second == vd.end())); if (is_equal) { return 0; } else { return ((*mismatch_pair.first > *mismatch_pair.second) ? 1 : -1); } } template <unsigned Digits10, class ExponentType, class Allocator> int cpp_dec_float<Digits10, ExponentType, Allocator>::compare(const cpp_dec_float& v) const { // Compare v with *this. // Return +1 for *this > v // 0 for *this = v // -1 for *this < v // Handle all non-finite cases. if ((!(isfinite)()) || (!(v.isfinite)())) { // NaN can never equal NaN. Return an implementation-dependent // signed result. Also note that comparison of NaN with NaN // using operators greater-than or less-than is undefined. if ((isnan)() || (v.isnan)()) { return ((isnan)() ? 1 : -1); } if ((isinf)() && (v.isinf)()) { // Both *this and v are infinite. They are equal if they have the same sign. // Otherwise, *this is less than v if and only if *this is negative. return ((neg == v.neg) ? 0 : (neg ? -1 : 1)); } if ((isinf)()) { // *this is infinite, but v is finite. // So negative infinite *this is less than any finite v. // Whereas positive infinite *this is greater than any finite v. return (isneg() ? -1 : 1); } else { // *this is finite, and v is infinite. // So any finite *this is greater than negative infinite v. // Whereas any finite *this is less than positive infinite v. return (v.neg ? 1 : -1); } } // And now handle all *finite* cases. if (iszero()) { // The value of *this is zero and v is either zero or non-zero. return (v.iszero() ? 0 : (v.neg ? 1 : -1)); } else if (v.iszero()) { // The value of v is zero and *this is non-zero. return (neg ? -1 : 1); } else { // Both *this and v are non-zero. if (neg != v.neg) { // The signs are different. return (neg ? -1 : 1); } else if (exp != v.exp) { // The signs are the same and the exponents are different. const int val_cexpression = ((exp < v.exp) ? 1 : -1); return (neg ? val_cexpression : -val_cexpression); } else { // The signs are the same and the exponents are the same. // Compare the data. const int val_cmp_data = cmp_data(v.data); return ((!neg) ? val_cmp_data : -val_cmp_data); } } } template <unsigned Digits10, class ExponentType, class Allocator> bool cpp_dec_float<Digits10, ExponentType, Allocator>::isone() const { // Check if the value of *this is identically 1 or very close to 1. const bool not_negative_and_is_finite = ((!neg) && (isfinite)()); if (not_negative_and_is_finite) { if ((data[0u] == static_cast<boost::uint32_t>(1u)) && (exp == static_cast<ExponentType>(0))) { const typename array_type::const_iterator it_non_zero = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate); return (it_non_zero == data.end()); } else if ((data[0u] == static_cast<boost::uint32_t>(cpp_dec_float_elem_mask - 1)) && (exp == static_cast<ExponentType>(-cpp_dec_float_elem_digits10))) { const typename array_type::const_iterator it_non_nine = std::find_if(data.begin(), data.end(), data_elem_is_non_nine_predicate); return (it_non_nine == data.end()); } } return false; } template <unsigned Digits10, class ExponentType, class Allocator> bool cpp_dec_float<Digits10, ExponentType, Allocator>::isint() const { if (fpclass != cpp_dec_float_finite) { return false; } if (iszero()) { return true; } if (exp < static_cast<ExponentType>(0)) { return false; } // |*this| < 1. const typename array_type::size_type offset_decimal_part = static_cast<typename array_type::size_type>(exp / cpp_dec_float_elem_digits10) + 1u; if (offset_decimal_part >= static_cast<typename array_type::size_type>(cpp_dec_float_elem_number)) { // The number is too large to resolve the integer part. // It considered to be a pure integer. return true; } typename array_type::const_iterator it_non_zero = std::find_if(data.begin() + offset_decimal_part, data.end(), data_elem_is_non_zero_predicate); return (it_non_zero == data.end()); } template <unsigned Digits10, class ExponentType, class Allocator> void cpp_dec_float<Digits10, ExponentType, Allocator>::extract_parts(double& mantissa, ExponentType& exponent) const { // Extract the approximate parts mantissa and base-10 exponent from the input cpp_dec_float<Digits10, ExponentType, Allocator> value x. // Extracts the mantissa and exponent. exponent = exp; boost::uint32_t p10 = static_cast<boost::uint32_t>(1u); boost::uint32_t test = data[0u]; for (;;) { test /= static_cast<boost::uint32_t>(10u); if (test == static_cast<boost::uint32_t>(0u)) { break; } p10 *= static_cast<boost::uint32_t>(10u); ++exponent; } // Establish the upper bound of limbs for extracting the double. const int max_elem_in_double_count = static_cast<int>(static_cast<boost::int32_t>(std::numeric_limits<double>::digits10) / cpp_dec_float_elem_digits10) + (static_cast<int>(static_cast<boost::int32_t>(std::numeric_limits<double>::digits10) % cpp_dec_float_elem_digits10) != 0 ? 1 : 0) + 1; // And make sure this upper bound stays within bounds of the elems. const std::size_t max_elem_extract_count = static_cast<std::size_t>((std::min)(static_cast<boost::int32_t>(max_elem_in_double_count), cpp_dec_float_elem_number)); // Extract into the mantissa the first limb, extracted as a double. mantissa = static_cast<double>(data[0]); double scale = 1.0; // Extract the rest of the mantissa piecewise from the limbs. for (std::size_t i = 1u; i < max_elem_extract_count; i++) { scale /= static_cast<double>(cpp_dec_float_elem_mask); mantissa += (static_cast<double>(data[i]) * scale); } mantissa /= static_cast<double>(p10); if (neg) { mantissa = -mantissa; } } template <unsigned Digits10, class ExponentType, class Allocator> double cpp_dec_float<Digits10, ExponentType, Allocator>::extract_double() const { // Returns the double conversion of a cpp_dec_float<Digits10, ExponentType, Allocator>. // Check for non-normal cpp_dec_float<Digits10, ExponentType, Allocator>. if (!(isfinite)()) { if ((isnan)()) { return std::numeric_limits<double>::quiet_NaN(); } else { return ((!neg) ? std::numeric_limits<double>::infinity() : -std::numeric_limits<double>::infinity()); } } cpp_dec_float<Digits10, ExponentType, Allocator> xx(*this); if (xx.isneg()) xx.negate(); // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is zero. if (iszero() || (xx.compare(double_min()) < 0)) { return 0.0; } // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> exceeds the maximum of double. if (xx.compare(double_max()) > 0) { return ((!neg) ? std::numeric_limits<double>::infinity() : -std::numeric_limits<double>::infinity()); } std::stringstream ss; ss << str(std::numeric_limits<double>::digits10 + (2 + 1), std::ios_base::scientific); double d; ss >> d; return d; } template <unsigned Digits10, class ExponentType, class Allocator> long double cpp_dec_float<Digits10, ExponentType, Allocator>::extract_long_double() const { // Returns the long double conversion of a cpp_dec_float<Digits10, ExponentType, Allocator>. // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is subnormal. if (!(isfinite)()) { if ((isnan)()) { return std::numeric_limits<long double>::quiet_NaN(); } else { return ((!neg) ? std::numeric_limits<long double>::infinity() : -std::numeric_limits<long double>::infinity()); } } cpp_dec_float<Digits10, ExponentType, Allocator> xx(*this); if (xx.isneg()) xx.negate(); // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is zero. if (iszero() || (xx.compare(long_double_min()) < 0)) { return static_cast<long double>(0.0); } // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> exceeds the maximum of double. if (xx.compare(long_double_max()) > 0) { return ((!neg) ? std::numeric_limits<long double>::infinity() : -std::numeric_limits<long double>::infinity()); } std::stringstream ss; ss << str(std::numeric_limits<long double>::digits10 + (2 + 1), std::ios_base::scientific); long double ld; ss >> ld; return ld; } template <unsigned Digits10, class ExponentType, class Allocator> boost::long_long_type cpp_dec_float<Digits10, ExponentType, Allocator>::extract_signed_long_long() const { // Extracts a signed long long from *this. // If (x > maximum of long long) or (x < minimum of long long), // then the maximum or minimum of long long is returned accordingly. if (exp < static_cast<ExponentType>(0)) { return static_cast<boost::long_long_type>(0); } const bool b_neg = isneg(); boost::ulong_long_type val; if ((!b_neg) && (compare(long_long_max()) > 0)) { return (std::numeric_limits<boost::long_long_type>::max)(); } else if (b_neg && (compare(long_long_min()) < 0)) { return (std::numeric_limits<boost::long_long_type>::min)(); } else { // Extract the data into an boost::ulong_long_type value. cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part()); if (xn.isneg()) xn.negate(); val = static_cast<boost::ulong_long_type>(xn.data[0]); const boost::int32_t imax = (std::min)(static_cast<boost::int32_t>(static_cast<boost::int32_t>(xn.exp) / cpp_dec_float_elem_digits10), static_cast<boost::int32_t>(cpp_dec_float_elem_number - static_cast<boost::int32_t>(1))); for (boost::int32_t i = static_cast<boost::int32_t>(1); i <= imax; i++) { val *= static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask); val += static_cast<boost::ulong_long_type>(xn.data[i]); } } if (!b_neg) { return static_cast<boost::long_long_type>(val); } else { // This strange expression avoids a hardware trap in the corner case // that val is the most negative value permitted in boost::long_long_type. // See https://svn.boost.org/trac/boost/ticket/9740. // boost::long_long_type sval = static_cast<boost::long_long_type>(val - 1); sval = -sval; --sval; return sval; } } template <unsigned Digits10, class ExponentType, class Allocator> boost::ulong_long_type cpp_dec_float<Digits10, ExponentType, Allocator>::extract_unsigned_long_long() const { // Extracts an boost::ulong_long_type from *this. // If x exceeds the maximum of boost::ulong_long_type, // then the maximum of boost::ulong_long_type is returned. // If x is negative, then the boost::ulong_long_type cast of // the long long extracted value is returned. if (isneg()) { return static_cast<boost::ulong_long_type>(extract_signed_long_long()); } if (exp < static_cast<ExponentType>(0)) { return static_cast<boost::ulong_long_type>(0u); } const cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part()); boost::ulong_long_type val; if (xn.compare(ulong_long_max()) > 0) { return (std::numeric_limits<boost::ulong_long_type>::max)(); } else { // Extract the data into an boost::ulong_long_type value. val = static_cast<boost::ulong_long_type>(xn.data[0]); const boost::int32_t imax = (std::min)(static_cast<boost::int32_t>(static_cast<boost::int32_t>(xn.exp) / cpp_dec_float_elem_digits10), static_cast<boost::int32_t>(cpp_dec_float_elem_number - static_cast<boost::int32_t>(1))); for (boost::int32_t i = static_cast<boost::int32_t>(1); i <= imax; i++) { val *= static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask); val += static_cast<boost::ulong_long_type>(xn.data[i]); } } return val; } template <unsigned Digits10, class ExponentType, class Allocator> cpp_dec_float<Digits10, ExponentType, Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>::extract_integer_part() const { // Compute the signed integer part of x. if (!(isfinite)()) { return *this; } if (exp < static_cast<ExponentType>(0)) { // The absolute value of the number is smaller than 1. // Thus the integer part is zero. return zero(); } // Truncate the digits from the decimal part, including guard digits // that do not belong to the integer part. // Make a local copy. cpp_dec_float<Digits10, ExponentType, Allocator> x = *this; // Clear out the decimal portion const size_t first_clear = (static_cast<size_t>(x.exp) / static_cast<size_t>(cpp_dec_float_elem_digits10)) + 1u; const size_t last_clear = static_cast<size_t>(cpp_dec_float_elem_number); if (first_clear < last_clear) std::fill(x.data.begin() + first_clear, x.data.begin() + last_clear, static_cast<boost::uint32_t>(0u)); return x; } template <unsigned Digits10, class ExponentType, class Allocator> std::string cpp_dec_float<Digits10, ExponentType, Allocator>::str(boost::intmax_t number_of_digits, std::ios_base::fmtflags f) const { if ((this->isinf)()) { if (this->isneg()) return "-inf"; else if (f & std::ios_base::showpos) return "+inf"; else return "inf"; } else if ((this->isnan)()) { return "nan"; } std::string str; boost::intmax_t org_digits(number_of_digits); ExponentType my_exp = order(); if (number_of_digits == 0) number_of_digits = cpp_dec_float_total_digits10; if (f & std::ios_base::fixed) { number_of_digits += my_exp + 1; } else if (f & std::ios_base::scientific) ++number_of_digits; // Determine the number of elements needed to provide the requested digits from cpp_dec_float<Digits10, ExponentType, Allocator>. const std::size_t number_of_elements = (std::min)(static_cast<std::size_t>((number_of_digits / static_cast<std::size_t>(cpp_dec_float_elem_digits10)) + 2u), static_cast<std::size_t>(cpp_dec_float_elem_number)); // Extract the remaining digits from cpp_dec_float<Digits10, ExponentType, Allocator> after the decimal point. str = boost::lexical_cast<std::string>(data[0]); std::stringstream ss; // Extract all of the digits from cpp_dec_float<Digits10, ExponentType, Allocator>, beginning with the first data element. for (std::size_t i = static_cast<std::size_t>(1u); i < number_of_elements; i++) { ss << std::setw(static_cast<std::streamsize>(cpp_dec_float_elem_digits10)) << std::setfill(static_cast<char>('0')) << data[i]; } str += ss.str(); bool have_leading_zeros = false; if (number_of_digits == 0) { // We only get here if the output format is "fixed" and we just need to // round the first non-zero digit. number_of_digits -= my_exp + 1; // reset to original value str.insert(static_cast<std::string::size_type>(0), std::string::size_type(number_of_digits), '0'); have_leading_zeros = true; } if (number_of_digits < 0) { str = "0"; if (isneg()) str.insert(static_cast<std::string::size_type>(0), 1, '-'); boost::multiprecision::detail::format_float_string(str, 0, number_of_digits - my_exp - 1, f, this->iszero()); return str; } else { // Cut the output to the size of the precision. if (str.length() > static_cast<std::string::size_type>(number_of_digits)) { // Get the digit after the last needed digit for rounding const boost::uint32_t round = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(str[static_cast<std::string::size_type>(number_of_digits)]) - static_cast<boost::uint32_t>('0')); bool need_round_up = round >= 5u; if (round == 5u) { const boost::uint32_t ix = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(str[static_cast<std::string::size_type>(number_of_digits - 1)]) - static_cast<boost::uint32_t>('0')); if ((ix & 1u) == 0) { // We have an even digit followed by a 5, so we might not actually need to round up // if all the remaining digits are zero: if (str.find_first_not_of('0', static_cast<std::string::size_type>(number_of_digits + 1)) == std::string::npos) { bool all_zeros = true; // No none-zero trailing digits in the string, now check whatever parts we didn't convert to the string: for (std::size_t i = number_of_elements; i < data.size(); i++) { if (data[i]) { all_zeros = false; break; } } if (all_zeros) need_round_up = false; // tie break - round to even. } } } // Truncate the string str.erase(static_cast<std::string::size_type>(number_of_digits)); if (need_round_up) { std::size_t ix = static_cast<std::size_t>(str.length() - 1u); // Every trailing 9 must be rounded up while (ix && (static_cast<boost::int32_t>(str.at(ix)) - static_cast<boost::int32_t>('0') == static_cast<boost::int32_t>(9))) { str.at(ix) = static_cast<char>('0'); --ix; } if (!ix) { // There were nothing but trailing nines. if (static_cast<boost::int32_t>(static_cast<boost::int32_t>(str.at(ix)) - static_cast<boost::int32_t>(0x30)) == static_cast<boost::int32_t>(9)) { // Increment up to the next order and adjust exponent. str.at(ix) = static_cast<char>('1'); ++my_exp; } else { // Round up this digit. ++str.at(ix); } } else { // Round up the last digit. ++str[ix]; } } } } if (have_leading_zeros) { // We need to take the zeros back out again, and correct the exponent // if we rounded up: if (str[std::string::size_type(number_of_digits - 1)] != '0') { ++my_exp; str.erase(0, std::string::size_type(number_of_digits - 1)); } else str.erase(0, std::string::size_type(number_of_digits)); } if (isneg()) str.insert(static_cast<std::string::size_type>(0), 1, '-'); boost::multiprecision::detail::format_float_string(str, my_exp, org_digits, f, this->iszero()); return str; } template <unsigned Digits10, class ExponentType, class Allocator> bool cpp_dec_float<Digits10, ExponentType, Allocator>::rd_string(const char* const s) { #ifndef BOOST_NO_EXCEPTIONS try { #endif std::string str(s); // TBD: Using several regular expressions may significantly reduce // the code complexity (and perhaps the run-time) of rd_string(). // Get a possible exponent and remove it. exp = static_cast<ExponentType>(0); std::size_t pos; if (((pos = str.find('e')) != std::string::npos) || ((pos = str.find('E')) != std::string::npos)) { // Remove the exponent part from the string. exp = boost::lexical_cast<ExponentType>(static_cast<const char*>(str.c_str() + (pos + 1u))); str = str.substr(static_cast<std::size_t>(0u), pos); } // Get a possible +/- sign and remove it. neg = false; if (str.size()) { if (str[0] == '-') { neg = true; str.erase(0, 1); } else if (str[0] == '+') { str.erase(0, 1); } } // // Special cases for infinities and NaN's: // if ((str == "inf") || (str == "INF") || (str == "infinity") || (str == "INFINITY")) { if (neg) { *this = this->inf(); this->negate(); } else *this = this->inf(); return true; } if ((str.size() >= 3) && ((str.substr(0, 3) == "nan") || (str.substr(0, 3) == "NAN") || (str.substr(0, 3) == "NaN"))) { *this = this->nan(); return true; } // Remove the leading zeros for all input types. const std::string::iterator fwd_it_leading_zero = std::find_if(str.begin(), str.end(), char_is_nonzero_predicate); if (fwd_it_leading_zero != str.begin()) { if (fwd_it_leading_zero == str.end()) { // The string contains nothing but leading zeros. // This string represents zero. operator=(zero()); return true; } else { str.erase(str.begin(), fwd_it_leading_zero); } } // Put the input string into the standard cpp_dec_float<Digits10, ExponentType, Allocator> input form // aaa.bbbbE+/-n, where aaa has 1...cpp_dec_float_elem_digits10, bbbb has an // even multiple of cpp_dec_float_elem_digits10 which are possibly zero padded // on the right-end, and n is a signed 64-bit integer which is an // even multiple of cpp_dec_float_elem_digits10. // Find a possible decimal point. pos = str.find(static_cast<char>('.')); if (pos != std::string::npos) { // Remove all trailing insignificant zeros. const std::string::const_reverse_iterator rit_non_zero = std::find_if(str.rbegin(), str.rend(), char_is_nonzero_predicate); if (rit_non_zero != static_cast<std::string::const_reverse_iterator>(str.rbegin())) { const std::string::size_type ofs = str.length() - std::distance<std::string::const_reverse_iterator>(str.rbegin(), rit_non_zero); str.erase(str.begin() + ofs, str.end()); } // Check if the input is identically zero. if (str == std::string(".")) { operator=(zero()); return true; } // Remove leading significant zeros just after the decimal point // and adjust the exponent accordingly. // Note that the while-loop operates only on strings of the form ".000abcd..." // and peels away the zeros just after the decimal point. if (str.at(static_cast<std::size_t>(0u)) == static_cast<char>('.')) { const std::string::iterator it_non_zero = std::find_if(str.begin() + 1u, str.end(), char_is_nonzero_predicate); std::size_t delta_exp = static_cast<std::size_t>(0u); if (str.at(static_cast<std::size_t>(1u)) == static_cast<char>('0')) { delta_exp = std::distance<std::string::const_iterator>(str.begin() + 1u, it_non_zero); } // Bring one single digit into the mantissa and adjust the exponent accordingly. str.erase(str.begin(), it_non_zero); str.insert(static_cast<std::string::size_type>(1u), "."); exp -= static_cast<ExponentType>(delta_exp + 1u); } } else { // Input string has no decimal point: Append decimal point. str.append("."); } // Shift the decimal point such that the exponent is an even multiple of cpp_dec_float_elem_digits10. std::size_t n_shift = static_cast<std::size_t>(0u); const std::size_t n_exp_rem = static_cast<std::size_t>(exp % static_cast<ExponentType>(cpp_dec_float_elem_digits10)); if ((exp % static_cast<ExponentType>(cpp_dec_float_elem_digits10)) != static_cast<ExponentType>(0)) { n_shift = ((exp < static_cast<ExponentType>(0)) ? static_cast<std::size_t>(n_exp_rem + static_cast<std::size_t>(cpp_dec_float_elem_digits10)) : static_cast<std::size_t>(n_exp_rem)); } // Make sure that there are enough digits for the decimal point shift. pos = str.find(static_cast<char>('.')); std::size_t pos_plus_one = static_cast<std::size_t>(pos + 1u); if ((str.length() - pos_plus_one) < n_shift) { const std::size_t sz = static_cast<std::size_t>(n_shift - (str.length() - pos_plus_one)); str.append(std::string(sz, static_cast<char>('0'))); } // Do the decimal point shift. if (n_shift != static_cast<std::size_t>(0u)) { str.insert(static_cast<std::string::size_type>(pos_plus_one + n_shift), "."); str.erase(pos, static_cast<std::string::size_type>(1u)); exp -= static_cast<ExponentType>(n_shift); } // Cut the size of the mantissa to <= cpp_dec_float_elem_digits10. pos = str.find(static_cast<char>('.')); pos_plus_one = static_cast<std::size_t>(pos + 1u); if (pos > static_cast<std::size_t>(cpp_dec_float_elem_digits10)) { const boost::int32_t n_pos = static_cast<boost::int32_t>(pos); const boost::int32_t n_rem_is_zero = ((static_cast<boost::int32_t>(n_pos % cpp_dec_float_elem_digits10) == static_cast<boost::int32_t>(0)) ? static_cast<boost::int32_t>(1) : static_cast<boost::int32_t>(0)); const boost::int32_t n = static_cast<boost::int32_t>(static_cast<boost::int32_t>(n_pos / cpp_dec_float_elem_digits10) - n_rem_is_zero); str.insert(static_cast<std::size_t>(static_cast<boost::int32_t>(n_pos - static_cast<boost::int32_t>(n * cpp_dec_float_elem_digits10))), "."); str.erase(pos_plus_one, static_cast<std::size_t>(1u)); exp += static_cast<ExponentType>(static_cast<ExponentType>(n) * static_cast<ExponentType>(cpp_dec_float_elem_digits10)); } // Pad the decimal part such that its value is an even // multiple of cpp_dec_float_elem_digits10. pos = str.find(static_cast<char>('.')); pos_plus_one = static_cast<std::size_t>(pos + 1u); const boost::int32_t n_dec = static_cast<boost::int32_t>(static_cast<boost::int32_t>(str.length() - 1u) - static_cast<boost::int32_t>(pos)); const boost::int32_t n_rem = static_cast<boost::int32_t>(n_dec % cpp_dec_float_elem_digits10); boost::int32_t n_cnt = ((n_rem != static_cast<boost::int32_t>(0)) ? static_cast<boost::int32_t>(cpp_dec_float_elem_digits10 - n_rem) : static_cast<boost::int32_t>(0)); if (n_cnt != static_cast<boost::int32_t>(0)) { str.append(static_cast<std::size_t>(n_cnt), static_cast<char>('0')); } // Truncate decimal part if it is too long. const std::size_t max_dec = static_cast<std::size_t>((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10); if (static_cast<std::size_t>(str.length() - pos) > max_dec) { str = str.substr(static_cast<std::size_t>(0u), static_cast<std::size_t>(pos_plus_one + max_dec)); } // Now the input string has the standard cpp_dec_float<Digits10, ExponentType, Allocator> input form. // (See the comment above.) // Set all the data elements to 0. std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u)); // Extract the data. // First get the digits to the left of the decimal point... data[0u] = boost::lexical_cast<boost::uint32_t>(str.substr(static_cast<std::size_t>(0u), pos)); // ...then get the remaining digits to the right of the decimal point. const std::string::size_type i_end = ((str.length() - pos_plus_one) / static_cast<std::string::size_type>(cpp_dec_float_elem_digits10)); for (std::string::size_type i = static_cast<std::string::size_type>(0u); i < i_end; i++) { const std::string::const_iterator it = str.begin() + pos_plus_one + (i * static_cast<std::string::size_type>(cpp_dec_float_elem_digits10)); data[i + 1u] = boost::lexical_cast<boost::uint32_t>(std::string(it, it + static_cast<std::string::size_type>(cpp_dec_float_elem_digits10))); } // Check for overflow... if (exp > cpp_dec_float_max_exp10) { const bool b_result_is_neg = neg; *this = inf(); if (b_result_is_neg) negate(); } // ...and check for underflow. if (exp <= cpp_dec_float_min_exp10) { if (exp == cpp_dec_float_min_exp10) { // Check for identity with the minimum value. cpp_dec_float<Digits10, ExponentType, Allocator> test = *this; test.exp = static_cast<ExponentType>(0); if (test.isone()) { *this = zero(); } } else { *this = zero(); } } #ifndef BOOST_NO_EXCEPTIONS } catch (const bad_lexical_cast&) { // Rethrow with better error message: std::string msg = "Unable to parse the string \""; msg += s; msg += "\" as a floating point value."; throw std::runtime_error(msg); } #endif return true; } template <unsigned Digits10, class ExponentType, class Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float(const double mantissa, const ExponentType exponent) : data(), exp(static_cast<ExponentType>(0)), neg(false), fpclass(cpp_dec_float_finite), prec_elem(cpp_dec_float_elem_number) { // Create *this cpp_dec_float<Digits10, ExponentType, Allocator> from a given mantissa and exponent. // Note: This constructor does not maintain the full precision of double. const bool mantissa_is_iszero = (::fabs(mantissa) < ((std::numeric_limits<double>::min)() * (1.0 + std::numeric_limits<double>::epsilon()))); if (mantissa_is_iszero) { std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u)); return; } const bool b_neg = (mantissa < 0.0); double d = ((!b_neg) ? mantissa : -mantissa); ExponentType e = exponent; while (d > 10.0) { d /= 10.0; ++e; } while (d < 1.0) { d *= 10.0; --e; } boost::int32_t shift = static_cast<boost::int32_t>(e % static_cast<boost::int32_t>(cpp_dec_float_elem_digits10)); while (static_cast<boost::int32_t>(shift-- % cpp_dec_float_elem_digits10) != static_cast<boost::int32_t>(0)) { d *= 10.0; --e; } exp = e; neg = b_neg; std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u)); static const boost::int32_t digit_ratio = static_cast<boost::int32_t>(static_cast<boost::int32_t>(std::numeric_limits<double>::digits10) / static_cast<boost::int32_t>(cpp_dec_float_elem_digits10)); static const boost::int32_t digit_loops = static_cast<boost::int32_t>(digit_ratio + static_cast<boost::int32_t>(2)); for (boost::int32_t i = static_cast<boost::int32_t>(0); i < digit_loops; i++) { boost::uint32_t n = static_cast<boost::uint32_t>(static_cast<boost::uint64_t>(d)); data[i] = static_cast<boost::uint32_t>(n); d -= static_cast<double>(n); d *= static_cast<double>(cpp_dec_float_elem_mask); } } template <unsigned Digits10, class ExponentType, class Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator=(long double a) { // Christopher Kormanyos's original code used a cast to boost::long_long_type here, but that fails // when long double has more digits than a boost::long_long_type. using std::floor; using std::frexp; using std::ldexp; if (a == 0) return *this = zero(); if (a == 1) return *this = one(); if ((boost::math::isinf)(a)) { *this = inf(); if (a < 0) this->negate(); return *this; } if ((boost::math::isnan)(a)) return *this = nan(); int e; long double f, term; *this = zero(); f = frexp(a, &e); // See https://svn.boost.org/trac/boost/ticket/10924 for an example of why this may go wrong: BOOST_ASSERT((boost::math::isfinite)(f)); static const int shift = std::numeric_limits<int>::digits - 1; while (f) { // extract int sized bits from f: f = ldexp(f, shift); BOOST_ASSERT((boost::math::isfinite)(f)); term = floor(f); e -= shift; *this *= pow2(shift); if (term > 0) add_unsigned_long_long(static_cast<unsigned>(term)); else sub_unsigned_long_long(static_cast<unsigned>(-term)); f -= term; } if (e != 0) *this *= pow2(e); return *this; } template <unsigned Digits10, class ExponentType, class Allocator> void cpp_dec_float<Digits10, ExponentType, Allocator>::from_unsigned_long_long(const boost::ulong_long_type u) { std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u)); exp = static_cast<ExponentType>(0); neg = false; fpclass = cpp_dec_float_finite; prec_elem = cpp_dec_float_elem_number; if (u == 0) { return; } std::size_t i = static_cast<std::size_t>(0u); boost::ulong_long_type uu = u; boost::uint32_t temp[(std::numeric_limits<boost::ulong_long_type>::digits10 / static_cast<int>(cpp_dec_float_elem_digits10)) + 3] = {static_cast<boost::uint32_t>(0u)}; while (uu != static_cast<boost::ulong_long_type>(0u)) { temp[i] = static_cast<boost::uint32_t>(uu % static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask)); uu = static_cast<boost::ulong_long_type>(uu / static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask)); ++i; } if (i > static_cast<std::size_t>(1u)) { exp += static_cast<ExponentType>((i - 1u) * static_cast<std::size_t>(cpp_dec_float_elem_digits10)); } std::reverse(temp, temp + i); std::copy(temp, temp + (std::min)(i, static_cast<std::size_t>(cpp_dec_float_elem_number)), data.begin()); } template <unsigned Digits10, class ExponentType, class Allocator> boost::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p) { // // There is a limit on how many limbs this algorithm can handle without dropping digits // due to overflow in the carry, it is: // // FLOOR( (2^64 - 1) / (10^8 * 10^8) ) == 1844 // BOOST_STATIC_ASSERT_MSG(cpp_dec_float_elem_number < 1800, "Too many limbs in the data type for the multiplication algorithm - unsupported precision in cpp_dec_float."); boost::uint64_t carry = static_cast<boost::uint64_t>(0u); for (boost::int32_t j = static_cast<boost::int32_t>(p - 1u); j >= static_cast<boost::int32_t>(0); j--) { boost::uint64_t sum = carry; for (boost::int32_t i = j; i >= static_cast<boost::int32_t>(0); i--) { sum += static_cast<boost::uint64_t>(u[j - i] * static_cast<boost::uint64_t>(v[i])); } u[j] = static_cast<boost::uint32_t>(sum % static_cast<boost::uint32_t>(cpp_dec_float_elem_mask)); carry = static_cast<boost::uint64_t>(sum / static_cast<boost::uint32_t>(cpp_dec_float_elem_mask)); } return static_cast<boost::uint32_t>(carry); } template <unsigned Digits10, class ExponentType, class Allocator> boost::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) { boost::uint64_t carry = static_cast<boost::uint64_t>(0u); // Multiplication loop. for (boost::int32_t j = p - 1; j >= static_cast<boost::int32_t>(0); j--) { const boost::uint64_t t = static_cast<boost::uint64_t>(carry + static_cast<boost::uint64_t>(u[j] * static_cast<boost::uint64_t>(n))); carry = static_cast<boost::uint64_t>(t / static_cast<boost::uint32_t>(cpp_dec_float_elem_mask)); u[j] = static_cast<boost::uint32_t>(t - static_cast<boost::uint64_t>(static_cast<boost::uint32_t>(cpp_dec_float_elem_mask) * static_cast<boost::uint64_t>(carry))); } return static_cast<boost::uint32_t>(carry); } template <unsigned Digits10, class ExponentType, class Allocator> boost::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) { boost::uint64_t prev = static_cast<boost::uint64_t>(0u); for (boost::int32_t j = static_cast<boost::int32_t>(0); j < p; j++) { const boost::uint64_t t = static_cast<boost::uint64_t>(u[j] + static_cast<boost::uint64_t>(prev * static_cast<boost::uint32_t>(cpp_dec_float_elem_mask))); u[j] = static_cast<boost::uint32_t>(t / n); prev = static_cast<boost::uint64_t>(t - static_cast<boost::uint64_t>(n * static_cast<boost::uint64_t>(u[j]))); } return static_cast<boost::uint32_t>(prev); } template <unsigned Digits10, class ExponentType, class Allocator> cpp_dec_float<Digits10, ExponentType, Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(const boost::long_long_type p) { // Create a static const table of p^2 for -128 < p < +128. // Note: The size of this table must be odd-numbered and // symmetric about 0. init.do_nothing(); static const boost::array<cpp_dec_float<Digits10, ExponentType, Allocator>, 255u> p2_data = {{cpp_dec_float("5.877471754111437539843682686111228389093327783860437607543758531392086297273635864257812500000000000e-39"), cpp_dec_float("1.175494350822287507968736537222245677818665556772087521508751706278417259454727172851562500000000000e-38"), cpp_dec_float("2.350988701644575015937473074444491355637331113544175043017503412556834518909454345703125000000000000e-38"), cpp_dec_float("4.701977403289150031874946148888982711274662227088350086035006825113669037818908691406250000000000000e-38"), cpp_dec_float("9.403954806578300063749892297777965422549324454176700172070013650227338075637817382812500000000000000e-38"), cpp_dec_float("1.880790961315660012749978459555593084509864890835340034414002730045467615127563476562500000000000000e-37"), cpp_dec_float("3.761581922631320025499956919111186169019729781670680068828005460090935230255126953125000000000000000e-37"), cpp_dec_float("7.523163845262640050999913838222372338039459563341360137656010920181870460510253906250000000000000000e-37"), cpp_dec_float("1.504632769052528010199982767644474467607891912668272027531202184036374092102050781250000000000000000e-36"), cpp_dec_float("3.009265538105056020399965535288948935215783825336544055062404368072748184204101562500000000000000000e-36"), cpp_dec_float("6.018531076210112040799931070577897870431567650673088110124808736145496368408203125000000000000000000e-36"), cpp_dec_float("1.203706215242022408159986214115579574086313530134617622024961747229099273681640625000000000000000000e-35"), cpp_dec_float("2.407412430484044816319972428231159148172627060269235244049923494458198547363281250000000000000000000e-35"), cpp_dec_float("4.814824860968089632639944856462318296345254120538470488099846988916397094726562500000000000000000000e-35"), cpp_dec_float("9.629649721936179265279889712924636592690508241076940976199693977832794189453125000000000000000000000e-35"), cpp_dec_float("1.925929944387235853055977942584927318538101648215388195239938795566558837890625000000000000000000000e-34"), cpp_dec_float("3.851859888774471706111955885169854637076203296430776390479877591133117675781250000000000000000000000e-34"), cpp_dec_float("7.703719777548943412223911770339709274152406592861552780959755182266235351562500000000000000000000000e-34"), cpp_dec_float("1.540743955509788682444782354067941854830481318572310556191951036453247070312500000000000000000000000e-33"), cpp_dec_float("3.081487911019577364889564708135883709660962637144621112383902072906494140625000000000000000000000000e-33"), cpp_dec_float("6.162975822039154729779129416271767419321925274289242224767804145812988281250000000000000000000000000e-33"), cpp_dec_float("1.232595164407830945955825883254353483864385054857848444953560829162597656250000000000000000000000000e-32"), cpp_dec_float("2.465190328815661891911651766508706967728770109715696889907121658325195312500000000000000000000000000e-32"), cpp_dec_float("4.930380657631323783823303533017413935457540219431393779814243316650390625000000000000000000000000000e-32"), cpp_dec_float("9.860761315262647567646607066034827870915080438862787559628486633300781250000000000000000000000000000e-32"), cpp_dec_float("1.972152263052529513529321413206965574183016087772557511925697326660156250000000000000000000000000000e-31"), cpp_dec_float("3.944304526105059027058642826413931148366032175545115023851394653320312500000000000000000000000000000e-31"), cpp_dec_float("7.888609052210118054117285652827862296732064351090230047702789306640625000000000000000000000000000000e-31"), cpp_dec_float("1.577721810442023610823457130565572459346412870218046009540557861328125000000000000000000000000000000e-30"), cpp_dec_float("3.155443620884047221646914261131144918692825740436092019081115722656250000000000000000000000000000000e-30"), cpp_dec_float("6.310887241768094443293828522262289837385651480872184038162231445312500000000000000000000000000000000e-30"), cpp_dec_float("1.262177448353618888658765704452457967477130296174436807632446289062500000000000000000000000000000000e-29"), cpp_dec_float("2.524354896707237777317531408904915934954260592348873615264892578125000000000000000000000000000000000e-29"), cpp_dec_float("5.048709793414475554635062817809831869908521184697747230529785156250000000000000000000000000000000000e-29"), cpp_dec_float("1.009741958682895110927012563561966373981704236939549446105957031250000000000000000000000000000000000e-28"), cpp_dec_float("2.019483917365790221854025127123932747963408473879098892211914062500000000000000000000000000000000000e-28"), cpp_dec_float("4.038967834731580443708050254247865495926816947758197784423828125000000000000000000000000000000000000e-28"), cpp_dec_float("8.077935669463160887416100508495730991853633895516395568847656250000000000000000000000000000000000000e-28"), cpp_dec_float("1.615587133892632177483220101699146198370726779103279113769531250000000000000000000000000000000000000e-27"), cpp_dec_float("3.231174267785264354966440203398292396741453558206558227539062500000000000000000000000000000000000000e-27"), cpp_dec_float("6.462348535570528709932880406796584793482907116413116455078125000000000000000000000000000000000000000e-27"), cpp_dec_float("1.292469707114105741986576081359316958696581423282623291015625000000000000000000000000000000000000000e-26"), cpp_dec_float("2.584939414228211483973152162718633917393162846565246582031250000000000000000000000000000000000000000e-26"), cpp_dec_float("5.169878828456422967946304325437267834786325693130493164062500000000000000000000000000000000000000000e-26"), cpp_dec_float("1.033975765691284593589260865087453566957265138626098632812500000000000000000000000000000000000000000e-25"), cpp_dec_float("2.067951531382569187178521730174907133914530277252197265625000000000000000000000000000000000000000000e-25"), cpp_dec_float("4.135903062765138374357043460349814267829060554504394531250000000000000000000000000000000000000000000e-25"), cpp_dec_float("8.271806125530276748714086920699628535658121109008789062500000000000000000000000000000000000000000000e-25"), cpp_dec_float("1.654361225106055349742817384139925707131624221801757812500000000000000000000000000000000000000000000e-24"), cpp_dec_float("3.308722450212110699485634768279851414263248443603515625000000000000000000000000000000000000000000000e-24"), cpp_dec_float("6.617444900424221398971269536559702828526496887207031250000000000000000000000000000000000000000000000e-24"), cpp_dec_float("1.323488980084844279794253907311940565705299377441406250000000000000000000000000000000000000000000000e-23"), cpp_dec_float("2.646977960169688559588507814623881131410598754882812500000000000000000000000000000000000000000000000e-23"), cpp_dec_float("5.293955920339377119177015629247762262821197509765625000000000000000000000000000000000000000000000000e-23"), cpp_dec_float("1.058791184067875423835403125849552452564239501953125000000000000000000000000000000000000000000000000e-22"), cpp_dec_float("2.117582368135750847670806251699104905128479003906250000000000000000000000000000000000000000000000000e-22"), cpp_dec_float("4.235164736271501695341612503398209810256958007812500000000000000000000000000000000000000000000000000e-22"), cpp_dec_float("8.470329472543003390683225006796419620513916015625000000000000000000000000000000000000000000000000000e-22"), cpp_dec_float("1.694065894508600678136645001359283924102783203125000000000000000000000000000000000000000000000000000e-21"), cpp_dec_float("3.388131789017201356273290002718567848205566406250000000000000000000000000000000000000000000000000000e-21"), cpp_dec_float("6.776263578034402712546580005437135696411132812500000000000000000000000000000000000000000000000000000e-21"), cpp_dec_float("1.355252715606880542509316001087427139282226562500000000000000000000000000000000000000000000000000000e-20"), cpp_dec_float("2.710505431213761085018632002174854278564453125000000000000000000000000000000000000000000000000000000e-20"), cpp_dec_float("5.421010862427522170037264004349708557128906250000000000000000000000000000000000000000000000000000000e-20"), cpp_dec_float("1.084202172485504434007452800869941711425781250000000000000000000000000000000000000000000000000000000e-19"), cpp_dec_float("2.168404344971008868014905601739883422851562500000000000000000000000000000000000000000000000000000000e-19"), cpp_dec_float("4.336808689942017736029811203479766845703125000000000000000000000000000000000000000000000000000000000e-19"), cpp_dec_float("8.673617379884035472059622406959533691406250000000000000000000000000000000000000000000000000000000000e-19"), cpp_dec_float("1.734723475976807094411924481391906738281250000000000000000000000000000000000000000000000000000000000e-18"), cpp_dec_float("3.469446951953614188823848962783813476562500000000000000000000000000000000000000000000000000000000000e-18"), cpp_dec_float("6.938893903907228377647697925567626953125000000000000000000000000000000000000000000000000000000000000e-18"), cpp_dec_float("1.387778780781445675529539585113525390625000000000000000000000000000000000000000000000000000000000000e-17"), cpp_dec_float("2.775557561562891351059079170227050781250000000000000000000000000000000000000000000000000000000000000e-17"), cpp_dec_float("5.551115123125782702118158340454101562500000000000000000000000000000000000000000000000000000000000000e-17"), cpp_dec_float("1.110223024625156540423631668090820312500000000000000000000000000000000000000000000000000000000000000e-16"), cpp_dec_float("2.220446049250313080847263336181640625000000000000000000000000000000000000000000000000000000000000000e-16"), cpp_dec_float("4.440892098500626161694526672363281250000000000000000000000000000000000000000000000000000000000000000e-16"), cpp_dec_float("8.881784197001252323389053344726562500000000000000000000000000000000000000000000000000000000000000000e-16"), cpp_dec_float("1.776356839400250464677810668945312500000000000000000000000000000000000000000000000000000000000000000e-15"), cpp_dec_float("3.552713678800500929355621337890625000000000000000000000000000000000000000000000000000000000000000000e-15"), cpp_dec_float("7.105427357601001858711242675781250000000000000000000000000000000000000000000000000000000000000000000e-15"), cpp_dec_float("1.421085471520200371742248535156250000000000000000000000000000000000000000000000000000000000000000000e-14"), cpp_dec_float("2.842170943040400743484497070312500000000000000000000000000000000000000000000000000000000000000000000e-14"), cpp_dec_float("5.684341886080801486968994140625000000000000000000000000000000000000000000000000000000000000000000000e-14"), cpp_dec_float("1.136868377216160297393798828125000000000000000000000000000000000000000000000000000000000000000000000e-13"), cpp_dec_float("2.273736754432320594787597656250000000000000000000000000000000000000000000000000000000000000000000000e-13"), cpp_dec_float("4.547473508864641189575195312500000000000000000000000000000000000000000000000000000000000000000000000e-13"), cpp_dec_float("9.094947017729282379150390625000000000000000000000000000000000000000000000000000000000000000000000000e-13"), cpp_dec_float("1.818989403545856475830078125000000000000000000000000000000000000000000000000000000000000000000000000e-12"), cpp_dec_float("3.637978807091712951660156250000000000000000000000000000000000000000000000000000000000000000000000000e-12"), cpp_dec_float("7.275957614183425903320312500000000000000000000000000000000000000000000000000000000000000000000000000e-12"), cpp_dec_float("1.455191522836685180664062500000000000000000000000000000000000000000000000000000000000000000000000000e-11"), cpp_dec_float("2.910383045673370361328125000000000000000000000000000000000000000000000000000000000000000000000000000e-11"), cpp_dec_float("5.820766091346740722656250000000000000000000000000000000000000000000000000000000000000000000000000000e-11"), cpp_dec_float("1.164153218269348144531250000000000000000000000000000000000000000000000000000000000000000000000000000e-10"), cpp_dec_float("2.328306436538696289062500000000000000000000000000000000000000000000000000000000000000000000000000000e-10"), cpp_dec_float("4.656612873077392578125000000000000000000000000000000000000000000000000000000000000000000000000000000e-10"), cpp_dec_float("9.313225746154785156250000000000000000000000000000000000000000000000000000000000000000000000000000000e-10"), cpp_dec_float("1.862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"), cpp_dec_float("3.725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"), cpp_dec_float("7.450580596923828125000000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"), cpp_dec_float("1.490116119384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"), cpp_dec_float("2.980232238769531250000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"), cpp_dec_float("5.960464477539062500000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"), cpp_dec_float("1.192092895507812500000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"), cpp_dec_float("2.384185791015625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"), cpp_dec_float("4.768371582031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"), cpp_dec_float("9.536743164062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"), cpp_dec_float("1.907348632812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"), cpp_dec_float("3.814697265625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"), cpp_dec_float("7.629394531250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"), cpp_dec_float("0.000015258789062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), cpp_dec_float("0.000030517578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), cpp_dec_float("0.000061035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), cpp_dec_float("0.000122070312500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), cpp_dec_float("0.000244140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), cpp_dec_float("0.000488281250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), cpp_dec_float("0.000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), cpp_dec_float("0.001953125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), cpp_dec_float("0.003906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), cpp_dec_float("0.007812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), cpp_dec_float("0.01562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), cpp_dec_float("0.03125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), cpp_dec_float("0.06250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), cpp_dec_float("0.125"), cpp_dec_float("0.25"), cpp_dec_float("0.5"), one(), two(), cpp_dec_float(static_cast<boost::ulong_long_type>(4)), cpp_dec_float(static_cast<boost::ulong_long_type>(8)), cpp_dec_float(static_cast<boost::ulong_long_type>(16)), cpp_dec_float(static_cast<boost::ulong_long_type>(32)), cpp_dec_float(static_cast<boost::ulong_long_type>(64)), cpp_dec_float(static_cast<boost::ulong_long_type>(128)), cpp_dec_float(static_cast<boost::ulong_long_type>(256)), cpp_dec_float(static_cast<boost::ulong_long_type>(512)), cpp_dec_float(static_cast<boost::ulong_long_type>(1024)), cpp_dec_float(static_cast<boost::ulong_long_type>(2048)), cpp_dec_float(static_cast<boost::ulong_long_type>(4096)), cpp_dec_float(static_cast<boost::ulong_long_type>(8192)), cpp_dec_float(static_cast<boost::ulong_long_type>(16384)), cpp_dec_float(static_cast<boost::ulong_long_type>(32768)), cpp_dec_float(static_cast<boost::ulong_long_type>(65536)), cpp_dec_float(static_cast<boost::ulong_long_type>(131072)), cpp_dec_float(static_cast<boost::ulong_long_type>(262144)), cpp_dec_float(static_cast<boost::ulong_long_type>(524288)), cpp_dec_float(static_cast<boost::uint64_t>(1uL << 20u)), cpp_dec_float(static_cast<boost::uint64_t>(1uL << 21u)), cpp_dec_float(static_cast<boost::uint64_t>(1uL << 22u)), cpp_dec_float(static_cast<boost::uint64_t>(1uL << 23u)), cpp_dec_float(static_cast<boost::uint64_t>(1uL << 24u)), cpp_dec_float(static_cast<boost::uint64_t>(1uL << 25u)), cpp_dec_float(static_cast<boost::uint64_t>(1uL << 26u)), cpp_dec_float(static_cast<boost::uint64_t>(1uL << 27u)), cpp_dec_float(static_cast<boost::uint64_t>(1uL << 28u)), cpp_dec_float(static_cast<boost::uint64_t>(1uL << 29u)), cpp_dec_float(static_cast<boost::uint64_t>(1uL << 30u)), cpp_dec_float(static_cast<boost::uint64_t>(1uL << 31u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 32u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 33u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 34u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 35u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 36u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 37u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 38u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 39u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 40u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 41u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 42u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 43u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 44u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 45u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 46u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 47u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 48u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 49u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 50u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 51u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 52u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 53u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 54u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 55u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 56u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 57u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 58u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 59u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 60u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 61u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 62u)), cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 63u)), cpp_dec_float("1.844674407370955161600000000000000000000000000000000000000000000000000000000000000000000000000000000e19"), cpp_dec_float("3.689348814741910323200000000000000000000000000000000000000000000000000000000000000000000000000000000e19"), cpp_dec_float("7.378697629483820646400000000000000000000000000000000000000000000000000000000000000000000000000000000e19"), cpp_dec_float("1.475739525896764129280000000000000000000000000000000000000000000000000000000000000000000000000000000e20"), cpp_dec_float("2.951479051793528258560000000000000000000000000000000000000000000000000000000000000000000000000000000e20"), cpp_dec_float("5.902958103587056517120000000000000000000000000000000000000000000000000000000000000000000000000000000e20"), cpp_dec_float("1.180591620717411303424000000000000000000000000000000000000000000000000000000000000000000000000000000e21"), cpp_dec_float("2.361183241434822606848000000000000000000000000000000000000000000000000000000000000000000000000000000e21"), cpp_dec_float("4.722366482869645213696000000000000000000000000000000000000000000000000000000000000000000000000000000e21"), cpp_dec_float("9.444732965739290427392000000000000000000000000000000000000000000000000000000000000000000000000000000e21"), cpp_dec_float("1.888946593147858085478400000000000000000000000000000000000000000000000000000000000000000000000000000e22"), cpp_dec_float("3.777893186295716170956800000000000000000000000000000000000000000000000000000000000000000000000000000e22"), cpp_dec_float("7.555786372591432341913600000000000000000000000000000000000000000000000000000000000000000000000000000e22"), cpp_dec_float("1.511157274518286468382720000000000000000000000000000000000000000000000000000000000000000000000000000e23"), cpp_dec_float("3.022314549036572936765440000000000000000000000000000000000000000000000000000000000000000000000000000e23"), cpp_dec_float("6.044629098073145873530880000000000000000000000000000000000000000000000000000000000000000000000000000e23"), cpp_dec_float("1.208925819614629174706176000000000000000000000000000000000000000000000000000000000000000000000000000e24"), cpp_dec_float("2.417851639229258349412352000000000000000000000000000000000000000000000000000000000000000000000000000e24"), cpp_dec_float("4.835703278458516698824704000000000000000000000000000000000000000000000000000000000000000000000000000e24"), cpp_dec_float("9.671406556917033397649408000000000000000000000000000000000000000000000000000000000000000000000000000e24"), cpp_dec_float("1.934281311383406679529881600000000000000000000000000000000000000000000000000000000000000000000000000e25"), cpp_dec_float("3.868562622766813359059763200000000000000000000000000000000000000000000000000000000000000000000000000e25"), cpp_dec_float("7.737125245533626718119526400000000000000000000000000000000000000000000000000000000000000000000000000e25"), cpp_dec_float("1.547425049106725343623905280000000000000000000000000000000000000000000000000000000000000000000000000e26"), cpp_dec_float("3.094850098213450687247810560000000000000000000000000000000000000000000000000000000000000000000000000e26"), cpp_dec_float("6.189700196426901374495621120000000000000000000000000000000000000000000000000000000000000000000000000e26"), cpp_dec_float("1.237940039285380274899124224000000000000000000000000000000000000000000000000000000000000000000000000e27"), cpp_dec_float("2.475880078570760549798248448000000000000000000000000000000000000000000000000000000000000000000000000e27"), cpp_dec_float("4.951760157141521099596496896000000000000000000000000000000000000000000000000000000000000000000000000e27"), cpp_dec_float("9.903520314283042199192993792000000000000000000000000000000000000000000000000000000000000000000000000e27"), cpp_dec_float("1.980704062856608439838598758400000000000000000000000000000000000000000000000000000000000000000000000e28"), cpp_dec_float("3.961408125713216879677197516800000000000000000000000000000000000000000000000000000000000000000000000e28"), cpp_dec_float("7.922816251426433759354395033600000000000000000000000000000000000000000000000000000000000000000000000e28"), cpp_dec_float("1.584563250285286751870879006720000000000000000000000000000000000000000000000000000000000000000000000e29"), cpp_dec_float("3.169126500570573503741758013440000000000000000000000000000000000000000000000000000000000000000000000e29"), cpp_dec_float("6.338253001141147007483516026880000000000000000000000000000000000000000000000000000000000000000000000e29"), cpp_dec_float("1.267650600228229401496703205376000000000000000000000000000000000000000000000000000000000000000000000e30"), cpp_dec_float("2.535301200456458802993406410752000000000000000000000000000000000000000000000000000000000000000000000e30"), cpp_dec_float("5.070602400912917605986812821504000000000000000000000000000000000000000000000000000000000000000000000e30"), cpp_dec_float("1.014120480182583521197362564300800000000000000000000000000000000000000000000000000000000000000000000e31"), cpp_dec_float("2.028240960365167042394725128601600000000000000000000000000000000000000000000000000000000000000000000e31"), cpp_dec_float("4.056481920730334084789450257203200000000000000000000000000000000000000000000000000000000000000000000e31"), cpp_dec_float("8.112963841460668169578900514406400000000000000000000000000000000000000000000000000000000000000000000e31"), cpp_dec_float("1.622592768292133633915780102881280000000000000000000000000000000000000000000000000000000000000000000e32"), cpp_dec_float("3.245185536584267267831560205762560000000000000000000000000000000000000000000000000000000000000000000e32"), cpp_dec_float("6.490371073168534535663120411525120000000000000000000000000000000000000000000000000000000000000000000e32"), cpp_dec_float("1.298074214633706907132624082305024000000000000000000000000000000000000000000000000000000000000000000e33"), cpp_dec_float("2.596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000e33"), cpp_dec_float("5.192296858534827628530496329220096000000000000000000000000000000000000000000000000000000000000000000e33"), cpp_dec_float("1.038459371706965525706099265844019200000000000000000000000000000000000000000000000000000000000000000e34"), cpp_dec_float("2.076918743413931051412198531688038400000000000000000000000000000000000000000000000000000000000000000e34"), cpp_dec_float("4.153837486827862102824397063376076800000000000000000000000000000000000000000000000000000000000000000e34"), cpp_dec_float("8.307674973655724205648794126752153600000000000000000000000000000000000000000000000000000000000000000e34"), cpp_dec_float("1.661534994731144841129758825350430720000000000000000000000000000000000000000000000000000000000000000e35"), cpp_dec_float("3.323069989462289682259517650700861440000000000000000000000000000000000000000000000000000000000000000e35"), cpp_dec_float("6.646139978924579364519035301401722880000000000000000000000000000000000000000000000000000000000000000e35"), cpp_dec_float("1.329227995784915872903807060280344576000000000000000000000000000000000000000000000000000000000000000e36"), cpp_dec_float("2.658455991569831745807614120560689152000000000000000000000000000000000000000000000000000000000000000e36"), cpp_dec_float("5.316911983139663491615228241121378304000000000000000000000000000000000000000000000000000000000000000e36"), cpp_dec_float("1.063382396627932698323045648224275660800000000000000000000000000000000000000000000000000000000000000e37"), cpp_dec_float("2.126764793255865396646091296448551321600000000000000000000000000000000000000000000000000000000000000e37"), cpp_dec_float("4.253529586511730793292182592897102643200000000000000000000000000000000000000000000000000000000000000e37"), cpp_dec_float("8.507059173023461586584365185794205286400000000000000000000000000000000000000000000000000000000000000e37"), cpp_dec_float("1.701411834604692317316873037158841057280000000000000000000000000000000000000000000000000000000000000e38")}}; if ((p > static_cast<boost::long_long_type>(-128)) && (p < static_cast<boost::long_long_type>(+128))) { return p2_data[static_cast<std::size_t>(p + ((p2_data.size() - 1u) / 2u))]; } else { // Compute and return 2^p. if (p < static_cast<boost::long_long_type>(0)) { return pow2(static_cast<boost::long_long_type>(-p)).calculate_inv(); } else { cpp_dec_float<Digits10, ExponentType, Allocator> t; default_ops::detail::pow_imp(t, two(), p, mpl::true_()); return t; } } } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o) { result += o; } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o) { result -= o; } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o) { result *= o; } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o) { result /= o; } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const boost::ulong_long_type& o) { result.add_unsigned_long_long(o); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const boost::ulong_long_type& o) { result.sub_unsigned_long_long(o); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const boost::ulong_long_type& o) { result.mul_unsigned_long_long(o); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const boost::ulong_long_type& o) { result.div_unsigned_long_long(o); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, boost::long_long_type o) { if (o < 0) result.sub_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o)); else result.add_unsigned_long_long(o); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, boost::long_long_type o) { if (o < 0) result.add_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o)); else result.sub_unsigned_long_long(o); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, boost::long_long_type o) { if (o < 0) { result.mul_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o)); result.negate(); } else result.mul_unsigned_long_long(o); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, boost::long_long_type o) { if (o < 0) { result.div_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o)); result.negate(); } else result.div_unsigned_long_long(o); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_convert_to(boost::ulong_long_type* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val) { *result = val.extract_unsigned_long_long(); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_convert_to(boost::long_long_type* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val) { *result = val.extract_signed_long_long(); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_convert_to(long double* result, cpp_dec_float<Digits10, ExponentType, Allocator>& val) { *result = val.extract_long_double(); } // // Non member function support: // template <unsigned Digits10, class ExponentType, class Allocator> inline int eval_fpclassify(const cpp_dec_float<Digits10, ExponentType, Allocator>& x) { if ((x.isinf)()) return FP_INFINITE; if ((x.isnan)()) return FP_NAN; if (x.iszero()) return FP_ZERO; return FP_NORMAL; } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_abs(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) { result = x; if (x.isneg()) result.negate(); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_fabs(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) { result = x; if (x.isneg()) result.negate(); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_sqrt(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) { result = x; result.calculate_sqrt(); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_floor(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) { result = x; if (!(x.isfinite)() || x.isint()) { if ((x.isnan)()) errno = EDOM; return; } if (x.isneg()) result -= cpp_dec_float<Digits10, ExponentType, Allocator>::one(); result = result.extract_integer_part(); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_ceil(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) { result = x; if (!(x.isfinite)() || x.isint()) { if ((x.isnan)()) errno = EDOM; return; } if (!x.isneg()) result += cpp_dec_float<Digits10, ExponentType, Allocator>::one(); result = result.extract_integer_part(); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_trunc(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) { if (x.isint() || !(x.isfinite)()) { result = x; if ((x.isnan)()) errno = EDOM; return; } result = x.extract_integer_part(); } template <unsigned Digits10, class ExponentType, class Allocator> inline ExponentType eval_ilogb(const cpp_dec_float<Digits10, ExponentType, Allocator>& val) { if (val.iszero()) return (std::numeric_limits<ExponentType>::min)(); if ((val.isinf)()) return INT_MAX; if ((val.isnan)()) #ifdef FP_ILOGBNAN return FP_ILOGBNAN; #else return INT_MAX; #endif // Set result, to the exponent of val: return val.order(); } template <unsigned Digits10, class ExponentType, class Allocator, class ArgType> inline void eval_scalbn(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val, ArgType e_) { using default_ops::eval_multiply; const ExponentType e = static_cast<ExponentType>(e_); cpp_dec_float<Digits10, ExponentType, Allocator> t(1.0, e); eval_multiply(result, val, t); } template <unsigned Digits10, class ExponentType, class Allocator, class ArgType> inline void eval_ldexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, ArgType e) { const boost::long_long_type the_exp = static_cast<boost::long_long_type>(e); if ((the_exp > (std::numeric_limits<ExponentType>::max)()) || (the_exp < (std::numeric_limits<ExponentType>::min)())) BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Exponent value is out of range."))); result = x; if ((the_exp > static_cast<boost::long_long_type>(-std::numeric_limits<boost::long_long_type>::digits)) && (the_exp < static_cast<boost::long_long_type>(0))) result.div_unsigned_long_long(1ULL << static_cast<boost::long_long_type>(-the_exp)); else if ((the_exp < static_cast<boost::long_long_type>(std::numeric_limits<boost::long_long_type>::digits)) && (the_exp > static_cast<boost::long_long_type>(0))) result.mul_unsigned_long_long(1ULL << the_exp); else if (the_exp != static_cast<boost::long_long_type>(0)) result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(e); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_frexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, ExponentType* e) { result = x; if (result.iszero() || (result.isinf)() || (result.isnan)()) { *e = 0; return; } if (result.isneg()) result.negate(); ExponentType t = result.order(); BOOST_MP_USING_ABS if (abs(t) < ((std::numeric_limits<ExponentType>::max)() / 1000)) { t *= 1000; t /= 301; } else { t /= 301; t *= 1000; } result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(-t); if (result.iszero() || (result.isinf)() || (result.isnan)()) { // pow2 overflowed, slip the calculation up: result = x; if (result.isneg()) result.negate(); t /= 2; result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(-t); } BOOST_MP_USING_ABS if (abs(result.order()) > 5) { // If our first estimate doesn't get close enough then try recursion until we do: ExponentType e2; cpp_dec_float<Digits10, ExponentType, Allocator> r2; eval_frexp(r2, result, &e2); // overflow protection: if ((t > 0) && (e2 > 0) && (t > (std::numeric_limits<ExponentType>::max)() - e2)) BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2.")); if ((t < 0) && (e2 < 0) && (t < (std::numeric_limits<ExponentType>::min)() - e2)) BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2.")); t += e2; result = r2; } while (result.compare(cpp_dec_float<Digits10, ExponentType, Allocator>::one()) >= 0) { result /= cpp_dec_float<Digits10, ExponentType, Allocator>::two(); ++t; } while (result.compare(cpp_dec_float<Digits10, ExponentType, Allocator>::half()) < 0) { result *= cpp_dec_float<Digits10, ExponentType, Allocator>::two(); --t; } *e = t; if (x.isneg()) result.negate(); } template <unsigned Digits10, class ExponentType, class Allocator> inline typename disable_if<is_same<ExponentType, int> >::type eval_frexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, int* e) { ExponentType t; eval_frexp(result, x, &t); if ((t > (std::numeric_limits<int>::max)()) || (t < (std::numeric_limits<int>::min)())) BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is outside the range of an int")); *e = static_cast<int>(t); } template <unsigned Digits10, class ExponentType, class Allocator> inline bool eval_is_zero(const cpp_dec_float<Digits10, ExponentType, Allocator>& val) { return val.iszero(); } template <unsigned Digits10, class ExponentType, class Allocator> inline int eval_get_sign(const cpp_dec_float<Digits10, ExponentType, Allocator>& val) { return val.iszero() ? 0 : val.isneg() ? -1 : 1; } template <unsigned Digits10, class ExponentType, class Allocator> inline std::size_t hash_value(const cpp_dec_float<Digits10, ExponentType, Allocator>& val) { return val.hash(); } } // namespace backends using boost::multiprecision::backends::cpp_dec_float; typedef number<cpp_dec_float<50> > cpp_dec_float_50; typedef number<cpp_dec_float<100> > cpp_dec_float_100; #ifdef BOOST_NO_SFINAE_EXPR namespace detail { template <unsigned D1, class E1, class A1, unsigned D2, class E2, class A2> struct is_explicitly_convertible<cpp_dec_float<D1, E1, A1>, cpp_dec_float<D2, E2, A2> > : public mpl::true_ {}; } // namespace detail #endif }} // namespace boost::multiprecision namespace std { template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> class numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> > { public: BOOST_STATIC_CONSTEXPR bool is_specialized = true; BOOST_STATIC_CONSTEXPR bool is_signed = true; BOOST_STATIC_CONSTEXPR bool is_integer = false; BOOST_STATIC_CONSTEXPR bool is_exact = false; BOOST_STATIC_CONSTEXPR bool is_bounded = true; BOOST_STATIC_CONSTEXPR bool is_modulo = false; BOOST_STATIC_CONSTEXPR bool is_iec559 = false; BOOST_STATIC_CONSTEXPR int digits = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10; BOOST_STATIC_CONSTEXPR int digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10; BOOST_STATIC_CONSTEXPR int max_digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_total_digits10; BOOST_STATIC_CONSTEXPR ExponentType min_exponent = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp; // Type differs from int. BOOST_STATIC_CONSTEXPR ExponentType min_exponent10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10; // Type differs from int. BOOST_STATIC_CONSTEXPR ExponentType max_exponent = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp; // Type differs from int. BOOST_STATIC_CONSTEXPR ExponentType max_exponent10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10; // Type differs from int. BOOST_STATIC_CONSTEXPR int radix = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_radix; BOOST_STATIC_CONSTEXPR std::float_round_style round_style = std::round_indeterminate; BOOST_STATIC_CONSTEXPR bool has_infinity = true; BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true; BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; BOOST_STATIC_CONSTEXPR std::float_denorm_style has_denorm = std::denorm_absent; BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; BOOST_STATIC_CONSTEXPR bool traps = false; BOOST_STATIC_CONSTEXPR bool tinyness_before = false; BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates>(min)() { return (boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::min)(); } BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates>(max)() { return (boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::max)(); } BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> lowest() { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); } BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> epsilon() { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::eps(); } BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> round_error() { return 0.5L; } BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> infinity() { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::inf(); } BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> quiet_NaN() { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::nan(); } BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> signaling_NaN() { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); } BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> denorm_min() { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); } }; #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::digits; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::digits10; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_digits10; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_signed; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_integer; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_exact; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::radix; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::min_exponent; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::min_exponent10; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_exponent; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_exponent10; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_infinity; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_quiet_NaN; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_signaling_NaN; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_denorm; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_denorm_loss; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_iec559; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_bounded; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_modulo; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::traps; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::tinyness_before; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::round_style; #endif } // namespace std namespace boost { namespace math { namespace policies { template <unsigned Digits10, class ExponentType, class Allocator, class Policy, boost::multiprecision::expression_template_option ExpressionTemplates> struct precision<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates>, Policy> { // Define a local copy of cpp_dec_float_digits10 because it might differ // from the template parameter Digits10 for small or large digit counts. static const boost::int32_t cpp_dec_float_digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10; typedef typename Policy::precision_type precision_type; typedef digits2<((cpp_dec_float_digits10 + 1LL) * 1000LL) / 301LL> digits_2; typedef typename mpl::if_c< ((digits_2::value <= precision_type::value) || (Policy::precision_type::value <= 0)), // Default case, full precision for RealType: digits_2, // User customized precision: precision_type>::type type; }; } }} // namespace boost::math::policies #ifdef BOOST_MSVC #pragma warning(pop) #endif #endif