boost/multiprecision/cpp_dec_float.hpp
/////////////////////////////////////////////////////////////////////////////// // Copyright Christopher Kormanyos 2002 - 2021. // Copyright 2011 -2021 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 // // There are some "noexcept" specifications on the functions in this file. // Unlike in pre-C++11 versions, compilers can now detect noexcept misuse // at compile time, allowing for simple use of it here. // #ifndef BOOST_MP_CPP_DEC_FLOAT_HPP #define BOOST_MP_CPP_DEC_FLOAT_HPP #include <cmath> #include <cstdint> #include <cstdlib> #include <algorithm> #include <array> #include <initializer_list> #include <iomanip> #include <string> #include <limits> #include <stdexcept> #include <sstream> #include <locale> #include <ios> #include <boost/multiprecision/detail/standalone_config.hpp> #include <boost/multiprecision/number.hpp> #include <boost/multiprecision/detail/fpclassify.hpp> #include <boost/multiprecision/detail/dynamic_array.hpp> #include <boost/multiprecision/detail/hash.hpp> #include <boost/multiprecision/detail/float128_functions.hpp> #include <boost/multiprecision/detail/itos.hpp> #include <boost/multiprecision/detail/static_array.hpp> #include <boost/multiprecision/detail/tables.hpp> #include <boost/multiprecision/detail/no_exceptions_support.hpp> #include <boost/multiprecision/detail/assert.hpp> #ifdef BOOST_MP_MATH_AVAILABLE // // 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/acosh.hpp> #include <boost/math/special_functions/asinh.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> #endif #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 = std::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 std::integral_constant<int, number_kind_floating_point> {}; namespace backends { template <unsigned Digits10, class ExponentType, class Allocator> class cpp_dec_float { private: // Perform some static sanity checks. static_assert(boost::multiprecision::detail::is_signed<ExponentType>::value, "ExponentType must be a signed built in integer type."); static_assert(sizeof(ExponentType) > 1, "ExponentType is too small."); static_assert(Digits10 < UINT32_C(0x80000000), "Digits10 exceeds the maximum."); // Private class-local constants. static constexpr std::int32_t cpp_dec_float_digits10_limit_lo = INT32_C(9); static constexpr std::int32_t cpp_dec_float_digits10_limit_hi = static_cast<std::int32_t>((std::numeric_limits<std::int32_t>::max)() - 100); static constexpr std::int32_t cpp_dec_float_elem_digits10 = INT32_C(8); static constexpr std::int32_t cpp_dec_float_elem_mask = INT32_C(100000000); static constexpr std::int32_t cpp_dec_float_elems_for_kara = static_cast<std::int32_t>(128 + 1); public: using signed_types = std::tuple<long long> ; using unsigned_types = std::tuple<unsigned long long>; using float_types = std::tuple<double, long double>; using exponent_type = ExponentType; // Public class-local constants. static constexpr std::int32_t cpp_dec_float_radix = INT32_C(10); static constexpr std::int32_t cpp_dec_float_digits10 = ((static_cast<std::int32_t>(Digits10) < cpp_dec_float_digits10_limit_lo) ? cpp_dec_float_digits10_limit_lo : ((static_cast<std::int32_t>(Digits10) > cpp_dec_float_digits10_limit_hi) ? cpp_dec_float_digits10_limit_hi : static_cast<std::int32_t>(Digits10))); static constexpr exponent_type cpp_dec_float_max_exp10 = (static_cast<exponent_type>(1) << (std::numeric_limits<exponent_type>::digits - 5)); static constexpr exponent_type cpp_dec_float_min_exp10 = -cpp_dec_float_max_exp10; static constexpr exponent_type cpp_dec_float_max_exp = cpp_dec_float_max_exp10; static constexpr exponent_type cpp_dec_float_min_exp = cpp_dec_float_min_exp10; static_assert(cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10 == -cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10, "Failed exponent range check"); static_assert(0 == cpp_dec_float_max_exp10 % cpp_dec_float_elem_digits10, "Failed digit sanity check"); private: // 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. static constexpr std::int32_t cpp_dec_float_elem_number = static_cast<std::int32_t>(((Digits10 / cpp_dec_float_elem_digits10) + (((Digits10 % cpp_dec_float_elem_digits10) != 0) ? 1 : 0)) + 3); public: static constexpr std::int32_t cpp_dec_float_max_digits10 = static_cast<std::int32_t>(cpp_dec_float_elem_number * cpp_dec_float_elem_digits10); private: using array_type = typename std::conditional<std::is_void<Allocator>::value, detail::static_array <std::uint32_t, static_cast<std::uint32_t>(cpp_dec_float_elem_number)>, detail::dynamic_array<std::uint32_t, static_cast<std::uint32_t>(cpp_dec_float_elem_number), Allocator> >::type; typedef enum enum_fpclass_type { cpp_dec_float_finite, cpp_dec_float_inf, cpp_dec_float_NaN } fpclass_type; array_type data; exponent_type exp; bool neg; fpclass_type fpclass; std::int32_t prec_elem; // Private constructor from the floating-point class type. explicit cpp_dec_float(fpclass_type c) : data(), exp(static_cast<exponent_type>(0)), neg(false), fpclass(c), prec_elem(cpp_dec_float_elem_number) {} // Constructor from an initializer_list, an optional // (value-aligned) exponent and a Boolean sign. static cpp_dec_float from_lst(std::initializer_list<std::uint32_t> lst, const exponent_type e = 0, const bool n = false) { cpp_dec_float a; a.data = array_type(lst); a.exp = e; a.neg = n; a.fpclass = cpp_dec_float_finite; a.prec_elem = cpp_dec_float_elem_number; return a; } public: // Public Constructors cpp_dec_float() noexcept(noexcept(array_type())) : data(), exp(static_cast<exponent_type>(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<exponent_type>(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 std::enable_if<boost::multiprecision::detail::is_unsigned<I>::value && (sizeof(I) <= sizeof(long long))>::type* = nullptr) : data(), exp(static_cast<exponent_type>(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 std::enable_if<( boost::multiprecision::detail::is_signed<I>::value && boost::multiprecision::detail::is_integral<I>::value && (sizeof(I) <= sizeof(long long)))>::type* = nullptr) : data(), exp(static_cast<exponent_type>(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(static_cast<unsigned long long>(i)); } cpp_dec_float(const cpp_dec_float& f) noexcept(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 std::enable_if<D <= Digits10>::type* = nullptr) : 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 std::enable_if< !(D <= Digits10)>::type* = nullptr) : 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 std::enable_if<std::is_floating_point<F>::value >::type* = nullptr) : data(), exp(static_cast<exponent_type>(0)), neg(false), fpclass(cpp_dec_float_finite), prec_elem(cpp_dec_float_elem_number) { *this = val; } cpp_dec_float(const double mantissa, const exponent_type exponent); std::size_t hash() const { std::size_t result = 0; for (int i = 0; i < prec_elem; ++i) boost::multiprecision::detail::hash_combine(result, data[i]); boost::multiprecision::detail::hash_combine(result, exp, neg, static_cast<std::size_t>(fpclass)); return result; } // Specific special values. static const cpp_dec_float& nan () { static const cpp_dec_float val(cpp_dec_float_NaN); return val; } static const cpp_dec_float& inf () { static const cpp_dec_float val(cpp_dec_float_inf); return val; } static const cpp_dec_float& (max)() { static const cpp_dec_float val(from_lst({ std::uint32_t(1u) }, cpp_dec_float_max_exp10)); return val; } static const cpp_dec_float& (min)() { static const cpp_dec_float val(from_lst({ std::uint32_t(1u) }, cpp_dec_float_min_exp10)); return val; } static const cpp_dec_float& zero() { static const cpp_dec_float val(from_lst({ std::uint32_t(0u) })); return val; } static const cpp_dec_float& one () { static const cpp_dec_float val(from_lst({ std::uint32_t(1u) })); return val; } static const cpp_dec_float& two () { static const cpp_dec_float val(from_lst({ std::uint32_t(2u) })); return val; } static const cpp_dec_float& half() { static const cpp_dec_float val(from_lst({ std::uint32_t(cpp_dec_float_elem_mask / 2)}, -8)); return val; } static const cpp_dec_float& double_min() { static const cpp_dec_float val((std::numeric_limits<double>::min)()); return val; } static const cpp_dec_float& double_max() { static const cpp_dec_float val((std::numeric_limits<double>::max)()); return val; } static const cpp_dec_float& long_double_min() { #ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS static const cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::min)())); #else static const cpp_dec_float val((std::numeric_limits<long double>::min)()); #endif return val; } static const cpp_dec_float& long_double_max() { #ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS static const cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::max)())); #else static const cpp_dec_float val((std::numeric_limits<long double>::max)()); #endif return val; } static const cpp_dec_float& long_long_max () { static const cpp_dec_float val((std::numeric_limits<long long>::max)()); return val; } static const cpp_dec_float& long_long_min () { static const cpp_dec_float val((std::numeric_limits<long long>::min)()); return val; } static const cpp_dec_float& ulong_long_max() { static const cpp_dec_float val((std::numeric_limits<unsigned long long>::max)()); return val; } static const cpp_dec_float& eps() { static const cpp_dec_float val ( from_lst ( { (std::uint32_t) detail::pow10_maker((std::uint32_t) ((std::int32_t) (INT32_C(1) + (std::int32_t) (((cpp_dec_float_digits10 / cpp_dec_float_elem_digits10) + ((cpp_dec_float_digits10 % cpp_dec_float_elem_digits10) != 0 ? 1 : 0)) * cpp_dec_float_elem_digits10)) - cpp_dec_float_digits10)) }, -(exponent_type) (((cpp_dec_float_digits10 / cpp_dec_float_elem_digits10) + ((cpp_dec_float_digits10 % cpp_dec_float_elem_digits10) != 0 ? 1 : 0)) * cpp_dec_float_elem_digits10) ) ); return val; } // Basic operations. cpp_dec_float& operator=(const cpp_dec_float& v) noexcept(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=(long long v) { if (v < 0) { from_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(v)); negate(); } else { using local_ulonglong_type = typename boost::multiprecision::detail::make_unsigned<long long>::type; from_unsigned_long_long(static_cast<local_ulonglong_type>(v)); } return *this; } cpp_dec_float& operator=(unsigned long long v) { from_unsigned_long_long(v); return *this; } #ifdef BOOST_HAS_INT128 cpp_dec_float& operator=(int128_type v) { *this = boost::multiprecision::detail::unsigned_abs(v); if (v < 0) negate(); return *this; } cpp_dec_float& operator=(uint128_type v) { using default_ops::eval_add; using default_ops::eval_multiply; constexpr unsigned bit_shift = sizeof(unsigned long long) * CHAR_BIT; constexpr uint128_type mask = (static_cast<uint128_type>(1u) << bit_shift) - 1; *this = static_cast<unsigned long long>(v & mask); v >>= bit_shift; while (v) { cpp_dec_float t(static_cast<unsigned long long>(v & mask)); eval_multiply(t, cpp_dec_float::pow2(bit_shift)); eval_add(*this, t); v >>= bit_shift; } return *this; } #endif template <class Float> typename std::enable_if<std::is_floating_point<Float>::value, cpp_dec_float&>::type operator=(Float 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 unsigned long long n) { cpp_dec_float t; t.from_unsigned_long_long(n); return *this += t; } cpp_dec_float& sub_unsigned_long_long(const unsigned long long n) { cpp_dec_float t; t.from_unsigned_long_long(n); return *this -= t; } cpp_dec_float& mul_unsigned_long_long(const unsigned long long n); cpp_dec_float& div_unsigned_long_long(const unsigned long long 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(std::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; long long extract_signed_long_long() const; unsigned long long extract_unsigned_long_long() const; #ifdef BOOST_HAS_INT128 int128_type extract_signed_int128() const; uint128_type extract_unsigned_int128() const; #endif void extract_parts(double& mantissa, exponent_type& exponent) const; cpp_dec_float extract_integer_part() const; void precision(const std::int32_t prec_digits) { const std::int32_t elems = static_cast<std::int32_t>( static_cast<std::int32_t>(prec_digits / cpp_dec_float_elem_digits10) + (((prec_digits % cpp_dec_float_elem_digits10) != 0) ? 1 : 0)); prec_elem = (std::min)(cpp_dec_float_elem_number, (std::max)(elems, static_cast<std::int32_t>(2))); } static cpp_dec_float pow2(long long i); exponent_type order() const { const bool bo_order_is_zero = ((!(isfinite)()) || (data[0] == static_cast<std::uint32_t>(0u))); // // Binary search to find the order of the leading term: // exponent_type 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<exponent_type>(0) : static_cast<exponent_type>(exp + prefix)); } #ifndef BOOST_MP_STANDALONE 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); } #endif private: static bool data_elem_is_non_zero_predicate(const std::uint32_t& d) { return (d != static_cast<std::uint32_t>(0u)); } static bool data_elem_is_non_nine_predicate(const std::uint32_t& d) { return (d != static_cast<std::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 unsigned long long u); template <typename InputIteratorTypeLeft, typename InputIteratorTypeRight> static int compare_ranges(InputIteratorTypeLeft a, InputIteratorTypeRight b, const std::uint32_t count = cpp_dec_float_elem_number); static std::uint32_t eval_add_n( std::uint32_t* r, const std::uint32_t* u, const std::uint32_t* v, const std::int32_t count); static std::uint32_t eval_subtract_n( std::uint32_t* r, const std::uint32_t* u, const std::uint32_t* v, const std::int32_t count); static void eval_multiply_n_by_n_to_2n( std::uint32_t* r, const std::uint32_t* a, const std::uint32_t* b, const std::uint32_t count); static std::uint32_t mul_loop_n(std::uint32_t* const u, std::uint32_t n, const std::int32_t p); static std::uint32_t div_loop_n(std::uint32_t* const u, std::uint32_t n, const std::int32_t p); static void eval_multiply_kara_propagate_carry (std::uint32_t* t, const std::uint32_t n, const std::uint32_t carry); static void eval_multiply_kara_propagate_borrow(std::uint32_t* t, const std::uint32_t n, const bool has_borrow); static void eval_multiply_kara_n_by_n_to_2n ( std::uint32_t* r, const std::uint32_t* a, const std::uint32_t* b, const std::uint32_t n, std::uint32_t* t); template<unsigned D> void eval_mul_dispatch_multiplication_method( const cpp_dec_float<D, ExponentType, Allocator>& v, const std::int32_t prec_elems_for_multiply, const typename std::enable_if< (D == Digits10) && (cpp_dec_float<D, ExponentType, Allocator>::cpp_dec_float_elem_number < cpp_dec_float_elems_for_kara)>::type* = nullptr) { // Use school multiplication. using array_for_mul_result_type = typename std::conditional<std::is_void<Allocator>::value, detail::static_array <std::uint32_t, std::uint32_t(cpp_dec_float_elem_number * 2)>, detail::dynamic_array<std::uint32_t, std::uint32_t(cpp_dec_float_elem_number * 2), Allocator> >::type; array_for_mul_result_type result; eval_multiply_n_by_n_to_2n(result.data(), data.data(), v.data.data(), static_cast<std::uint32_t>(prec_elems_for_multiply)); // Handle a potential carry. if(result[0U] != static_cast<std::uint32_t>(0U)) { exp += static_cast<exponent_type>(cpp_dec_float_elem_digits10); // Shift the result of the multiplication one element to the right. std::copy(result.cbegin(), result.cbegin() + static_cast<std::ptrdiff_t>(prec_elems_for_multiply), data.begin()); } else { std::copy(result.cbegin() + 1, result.cbegin() + (std::min)(static_cast<std::int32_t>(prec_elems_for_multiply + 1), cpp_dec_float_elem_number), data.begin()); } } template<unsigned D> void eval_mul_dispatch_multiplication_method( const cpp_dec_float<D, ExponentType, Allocator>& v, const std::int32_t prec_elems_for_multiply, const typename std::enable_if< (D == Digits10) && !(cpp_dec_float<D, ExponentType, Allocator>::cpp_dec_float_elem_number < cpp_dec_float_elems_for_kara)>::type* = nullptr) { if(prec_elems_for_multiply < cpp_dec_float_elems_for_kara) { // Use school multiplication. using array_for_mul_result_type = typename std::conditional<std::is_void<Allocator>::value, detail::static_array <std::uint32_t, std::uint32_t(cpp_dec_float_elem_number * 2)>, detail::dynamic_array<std::uint32_t, std::uint32_t(cpp_dec_float_elem_number * 2), Allocator> >::type; array_for_mul_result_type result; eval_multiply_n_by_n_to_2n(result.data(), data.data(), v.data.data(), static_cast<std::uint32_t>(prec_elems_for_multiply)); // Handle a potential carry. if(result[0U] != static_cast<std::uint32_t>(0U)) { exp += static_cast<exponent_type>(cpp_dec_float_elem_digits10); // Shift the result of the multiplication one element to the right. std::copy(result.cbegin(), result.cbegin() + static_cast<std::ptrdiff_t>(prec_elems_for_multiply), data.begin()); } else { std::copy(result.cbegin() + 1, result.cbegin() + (std::min)(static_cast<std::int32_t>(prec_elems_for_multiply + 1), cpp_dec_float_elem_number), data.begin()); } } else { // Use Karatsuba multiplication. using array_for_kara_tmp_type = typename std::conditional<std::is_void<Allocator>::value, detail::static_array <std::uint32_t, detail::a029750::a029750_as_constexpr(static_cast<std::uint32_t>(cpp_dec_float_elem_number)) * 8U>, detail::dynamic_array<std::uint32_t, detail::a029750::a029750_as_constexpr(static_cast<std::uint32_t>(cpp_dec_float_elem_number)) * 8U, Allocator> >::type; // Sloanes's A029747: Numbers of the form 2^k times 1, 3 or 5. const std::uint32_t kara_elems_for_multiply = detail::a029750::a029750_as_runtime_value(static_cast<std::uint32_t>(prec_elems_for_multiply)); array_for_kara_tmp_type my_kara_mul_pool; std::uint32_t* result = my_kara_mul_pool.data() + (kara_elems_for_multiply * 0U); std::uint32_t* t = my_kara_mul_pool.data() + (kara_elems_for_multiply * 2U); std::uint32_t* u_local = my_kara_mul_pool.data() + (kara_elems_for_multiply * 6U); std::uint32_t* v_local = my_kara_mul_pool.data() + (kara_elems_for_multiply * 7U); std::copy( data.cbegin(), data.cbegin() + prec_elems_for_multiply, u_local); std::copy(v.data.cbegin(), v.data.cbegin() + prec_elems_for_multiply, v_local); eval_multiply_kara_n_by_n_to_2n(result, u_local, v_local, kara_elems_for_multiply, t); // Handle a potential carry. if(result[0U] != static_cast<std::uint32_t>(0U)) { exp += static_cast<exponent_type>(cpp_dec_float_elem_digits10); // Shift the result of the multiplication one element to the right. std::copy(result, result + static_cast<std::ptrdiff_t>(prec_elems_for_multiply), data.begin()); } else { std::copy(result + 1, result + (std::min)(static_cast<std::int32_t>(prec_elems_for_multiply + 1), cpp_dec_float_elem_number), data.begin()); } } } 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> constexpr std::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_radix; template <unsigned Digits10, class ExponentType, class Allocator> constexpr std::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_limit_lo; template <unsigned Digits10, class ExponentType, class Allocator> constexpr std::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_limit_hi; template <unsigned Digits10, class ExponentType, class Allocator> constexpr std::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10; template <unsigned Digits10, class ExponentType, class Allocator> constexpr ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp; template <unsigned Digits10, class ExponentType, class Allocator> constexpr ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp; template <unsigned Digits10, class ExponentType, class Allocator> constexpr ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10; template <unsigned Digits10, class ExponentType, class Allocator> constexpr ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10; template <unsigned Digits10, class ExponentType, class Allocator> constexpr std::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_digits10; template <unsigned Digits10, class ExponentType, class Allocator> constexpr std::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_number; template <unsigned Digits10, class ExponentType, class Allocator> constexpr std::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. constexpr exponent_type max_delta_exp = static_cast<exponent_type>((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10); const exponent_type ofs_exp = static_cast<exponent_type>(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::pointer p_u = data.data(); typename array_type::const_pointer p_v = v.data.data(); bool b_copy = false; const std::int32_t ofs = static_cast<std::int32_t>(static_cast<std::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<std::int32_t>(0)) { std::copy(v.data.cbegin(), v.data.cend() - static_cast<std::ptrdiff_t>(ofs), n_data.begin() + static_cast<std::ptrdiff_t>(ofs)); std::fill(n_data.begin(), n_data.begin() + static_cast<std::ptrdiff_t>(ofs), static_cast<std::uint32_t>(0u)); p_v = n_data.data(); } else { std::copy(data.cbegin(), data.cend() - static_cast<std::ptrdiff_t>(-ofs), n_data.begin() + static_cast<std::ptrdiff_t>(-ofs)); std::fill(n_data.begin(), n_data.begin() + static_cast<std::ptrdiff_t>(-ofs), static_cast<std::uint32_t>(0u)); p_u = n_data.data(); b_copy = true; } // Addition algorithm const std::uint32_t carry = eval_add_n(p_u, p_u, p_v, cpp_dec_float_elem_number); 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<std::uint32_t>(0u)) { std::copy_backward(data.cbegin(), data.cend() - static_cast<std::size_t>(1u), data.end()); data[0] = carry; exp += static_cast<exponent_type>(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<std::int32_t>(0)) || ((ofs == static_cast<std::int32_t>(0)) && (compare_ranges(data.cbegin(), v.data.cbegin()) > static_cast<std::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.cbegin(), v.data.cend() - static_cast<std::ptrdiff_t>(ofs), n_data.begin() + static_cast<std::ptrdiff_t>(ofs)); std::fill(n_data.begin(), n_data.begin() + static_cast<std::ptrdiff_t>(ofs), static_cast<std::uint32_t>(0u)); p_v = n_data.data(); } else { if (ofs != static_cast<std::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.cbegin(), data.cend() - static_cast<std::ptrdiff_t>(-ofs), data.end()); std::fill(data.begin(), data.begin() + static_cast<std::ptrdiff_t>(-ofs), static_cast<std::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.data(); p_v = data.data(); b_copy = true; } // Subtraction algorithm static_cast<void>(eval_subtract_n(p_u, p_u, p_v, cpp_dec_float_elem_number)); 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<exponent_type>(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::ptrdiff_t>(sj), data.end(), data.begin()); std::fill(data.end() - static_cast<std::ptrdiff_t>(sj), data.end(), static_cast<std::uint32_t>(0u)); exp -= static_cast<exponent_type>(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<exponent_type>(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<exponent_type>(cpp_dec_float_max_exp10)); const bool b_result_might_underflow = ((exp + v.exp) <= static_cast<exponent_type>(cpp_dec_float_min_exp10)); // Set the exponent of the result. exp += v.exp; const std::int32_t prec_mul = (std::min)(prec_elem, v.prec_elem); eval_mul_dispatch_multiplication_method(v, prec_mul); // 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) && (compare_ranges(data.cbegin(), v.data.cbegin()) == static_cast<std::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 unsigned long long n) { // Multiply *this with a constant unsigned long long. // 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<std::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<unsigned long long>(cpp_dec_float_elem_mask)) { neg = b_neg; cpp_dec_float t; t = n; return operator*=(t); } if (n == static_cast<unsigned long long>(1u)) { neg = b_neg; return *this; } // Set up the multiplication loop. const std::uint32_t nn = static_cast<std::uint32_t>(n); const std::uint32_t carry = mul_loop_n(data.data(), nn, prec_elem); // Handle the carry and adjust the exponent. if (carry != static_cast<std::uint32_t>(0u)) { exp += static_cast<exponent_type>(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::ptrdiff_t>(prec_elem - static_cast<std::int32_t>(1)), data.begin() + static_cast<std::ptrdiff_t>(prec_elem)); data.front() = static_cast<std::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 unsigned long long n) { // Divide *this by a constant unsigned long long. // 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<unsigned long long>(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<unsigned long long>(cpp_dec_float_elem_mask)) { neg = b_neg; cpp_dec_float t; t = n; return operator/=(t); } const std::uint32_t nn = static_cast<std::uint32_t>(n); if (nn > static_cast<std::uint32_t>(1u)) { // Do the division loop. const std::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<std::uint32_t>(0u)) { // Adjust the exponent exp -= static_cast<exponent_type>(cpp_dec_float_elem_digits10); // Shift result of the division one element to the left. std::copy(data.begin() + static_cast<std::ptrdiff_t>(1), data.begin() + static_cast<std::ptrdiff_t>(prec_elem - static_cast<std::int32_t>(1)), data.begin()); data[static_cast<std::size_t>(prec_elem - static_cast<std::int32_t>(1))] = static_cast<std::uint32_t>(static_cast<std::uint64_t>(prev * static_cast<std::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; exponent_type 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. constexpr std::int32_t double_digits10_minus_a_few = std::numeric_limits<double>::digits10 - 3; for (std::int32_t digits = double_digits10_minus_a_few; digits <= cpp_dec_float_max_digits10; digits *= static_cast<std::int32_t>(2)) { // Adjust precision of the terms. precision(static_cast<std::int32_t>((digits + 10) * static_cast<std::int32_t>(2))); x.precision(static_cast<std::int32_t>((digits + 10) * static_cast<std::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; exponent_type ne; extract_parts(dd, ne); // Force the exponent to be an even multiple of two. if ((ne % static_cast<exponent_type>(2)) != static_cast<exponent_type>(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 reference to "Pi Unleashed: // https://www.springer.com/gp/book/9783642567353 constexpr std::uint32_t double_digits10_minus_a_few = std::numeric_limits<double>::digits10 - 3; for (std::int32_t digits = double_digits10_minus_a_few; digits <= cpp_dec_float_max_digits10; digits *= 2) { // 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>::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 = compare_ranges(data.cbegin(), v.data.cbegin()); 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<std::uint32_t>(1u)) && (exp == static_cast<exponent_type>(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<std::uint32_t>(cpp_dec_float_elem_mask - 1)) && (exp == static_cast<exponent_type>(-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<exponent_type>(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() + static_cast<std::ptrdiff_t>(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; std::uint32_t p10 = static_cast<std::uint32_t>(1u); std::uint32_t test = data[0u]; for (;;) { test /= static_cast<std::uint32_t>(10u); if (test == static_cast<std::uint32_t>(0u)) { break; } p10 *= static_cast<std::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<std::int32_t>(std::numeric_limits<double>::digits10) / cpp_dec_float_elem_digits10) + (static_cast<int>(static_cast<std::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<std::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.imbue(std::locale::classic()); 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.imbue(std::locale::classic()); 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> long long 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<exponent_type>(0)) { return static_cast<long long>(0); } const bool b_neg = isneg(); unsigned long long val; if ((!b_neg) && (compare(long_long_max()) > 0)) { return (std::numeric_limits<long long>::max)(); } else if (b_neg && (compare(long_long_min()) < 0)) { return (std::numeric_limits<long long>::min)(); } else { // Extract the data into an unsigned long long value. cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part()); if (xn.isneg()) xn.negate(); val = static_cast<unsigned long long>(xn.data[0]); const std::int32_t imax = (std::min)(static_cast<std::int32_t>(static_cast<std::int32_t>(xn.exp) / cpp_dec_float_elem_digits10), static_cast<std::int32_t>(cpp_dec_float_elem_number - static_cast<std::int32_t>(1))); for (std::int32_t i = static_cast<std::int32_t>(1); i <= imax; i++) { val *= static_cast<unsigned long long>(cpp_dec_float_elem_mask); val += static_cast<unsigned long long>(xn.data[static_cast<std::size_t>(i)]); } } if (!b_neg) { return static_cast<long long>(val); } else { // This strange expression avoids a hardware trap in the corner case // that val is the most negative value permitted in long long. // See https://svn.boost.org/trac/boost/ticket/9740. // long long sval = static_cast<long long>(val - 1); sval = -sval; --sval; return sval; } } template <unsigned Digits10, class ExponentType, class Allocator> unsigned long long cpp_dec_float<Digits10, ExponentType, Allocator>::extract_unsigned_long_long() const { // Extracts an unsigned long long from *this. // If x exceeds the maximum of unsigned long long, // then the maximum of unsigned long long is returned. // If x is negative, then the unsigned long long cast of // the long long extracted value is returned. if (isneg()) { return static_cast<unsigned long long>(extract_signed_long_long()); } if (exp < static_cast<exponent_type>(0)) { return static_cast<unsigned long long>(0u); } const cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part()); unsigned long long val; if (xn.compare(ulong_long_max()) > 0) { return (std::numeric_limits<unsigned long long>::max)(); } else { // Extract the data into an unsigned long long value. val = static_cast<unsigned long long>(xn.data[0]); const std::int32_t imax = (std::min)(static_cast<std::int32_t>(static_cast<std::int32_t>(xn.exp) / cpp_dec_float_elem_digits10), static_cast<std::int32_t>(cpp_dec_float_elem_number - static_cast<std::int32_t>(1))); for (std::int32_t i = static_cast<std::int32_t>(1); i <= imax; i++) { val *= static_cast<unsigned long long>(cpp_dec_float_elem_mask); val += static_cast<unsigned long long>(xn.data[i]); } } return val; } #ifdef BOOST_HAS_INT128 template <unsigned Digits10, class ExponentType, class Allocator> int128_type cpp_dec_float<Digits10, ExponentType, Allocator>::extract_signed_int128() const { // Extracts a signed __int128 from *this. // If (x > maximum of __int128) or (x < minimum of __int128), // then the maximum or minimum of long long is returned accordingly. if (exp < static_cast<exponent_type>(0)) { return static_cast<int128_type>(0); } const bool b_neg = isneg(); cpp_dec_float<Digits10, ExponentType, Allocator> i128max; i128max = ((~static_cast<uint128_type>(0)) >> 1); cpp_dec_float<Digits10, ExponentType, Allocator> i128min; i128min = (-1 - static_cast<int128_type>((static_cast<uint128_type>(1) << 127) - 1)); uint128_type val; if ((!b_neg) && (compare(i128max) > 0)) { return ((~static_cast<uint128_type>(0)) >> 1); } else if (b_neg && (compare(i128min) < 0)) { return (-1 - static_cast<int128_type>((static_cast<uint128_type>(1) << 127) - 1)); } else { // Extract the data into an unsigned long long value. cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part()); if (xn.isneg()) xn.negate(); val = static_cast<uint128_type>(xn.data[0]); const std::int32_t imax = (std::min)(static_cast<std::int32_t>(static_cast<std::int32_t>(xn.exp) / cpp_dec_float_elem_digits10), static_cast<std::int32_t>(cpp_dec_float_elem_number - static_cast<std::int32_t>(1))); for (std::int32_t i = static_cast<std::int32_t>(1); i <= imax; i++) { val *= static_cast<uint128_type>(cpp_dec_float_elem_mask); val += static_cast<uint128_type>(xn.data[static_cast<std::size_t>(i)]); } } if (!b_neg) { return static_cast<int128_type>(val); } else { // This strange expression avoids a hardware trap in the corner case // that val is the most negative value permitted in long long. // See https://svn.boost.org/trac/boost/ticket/9740. // int128_type sval = static_cast<int128_type>(val - 1); sval = -sval; --sval; return sval; } } template <unsigned Digits10, class ExponentType, class Allocator> uint128_type cpp_dec_float<Digits10, ExponentType, Allocator>::extract_unsigned_int128() const { // Extracts an unsigned __int128 from *this. // If x exceeds the maximum of unsigned __int128, // then the maximum of unsigned __int128 is returned. // If x is negative, then the unsigned __int128 cast of // the __int128 extracted value is returned. if (isneg()) { return static_cast<uint128_type>(extract_signed_int128()); } if (exp < static_cast<exponent_type>(0)) { return 0u; } const cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part()); cpp_dec_float<Digits10, ExponentType, Allocator> i128max; i128max = (~static_cast<uint128_type>(0)); uint128_type val; if (xn.compare(i128max) > 0) { return (~static_cast<uint128_type>(0)); } else { // Extract the data into an unsigned long long value. val = static_cast<uint128_type>(xn.data[0]); const std::int32_t imax = (std::min)(static_cast<std::int32_t>(static_cast<std::int32_t>(xn.exp) / cpp_dec_float_elem_digits10), static_cast<std::int32_t>(cpp_dec_float_elem_number - static_cast<std::int32_t>(1))); for (std::int32_t i = static_cast<std::int32_t>(1); i <= imax; i++) { val *= static_cast<uint128_type>(cpp_dec_float_elem_mask); val += static_cast<uint128_type>(xn.data[i]); } } return val; } #endif 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 std::size_t first_clear = (static_cast<std::size_t>(x.exp) / static_cast<std::size_t>(cpp_dec_float_elem_digits10)) + 1u; const std::size_t last_clear = static_cast<std::size_t>(cpp_dec_float_elem_number); if (first_clear < last_clear) std::fill(x.data.begin() + static_cast<std::ptrdiff_t>(first_clear), x.data.begin() + static_cast<std::ptrdiff_t>(last_clear), static_cast<std::uint32_t>(0u)); return x; } template <unsigned Digits10, class ExponentType, class Allocator> std::string cpp_dec_float<Digits10, ExponentType, Allocator>::str(std::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; std::intmax_t org_digits(number_of_digits); exponent_type my_exp = order(); if (!(f & std::ios_base::fixed) && (number_of_digits == 0)) number_of_digits = cpp_dec_float_max_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>(static_cast<std::size_t>(number_of_digits / static_cast<std::intmax_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. std::stringstream ss; ss.imbue(std::locale::classic()); ss << data[0]; // 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 if (number_of_digits) { 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 std::uint32_t round = static_cast<std::uint32_t>(static_cast<std::uint32_t>(str[static_cast<std::string::size_type>(number_of_digits)]) - static_cast<std::uint32_t>('0')); bool need_round_up = round >= 5u; if (round == 5u) { const std::uint32_t ix = number_of_digits == 0 ? 0 : static_cast<std::uint32_t>(static_cast<std::uint32_t>(str[static_cast<std::string::size_type>(number_of_digits - 1)]) - static_cast<std::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) { if (str.size()) { std::size_t ix = static_cast<std::size_t>(str.length() - 1u); // Every trailing 9 must be rounded up while (ix && (static_cast<std::int32_t>(str.at(ix)) - static_cast<std::int32_t>('0') == static_cast<std::int32_t>(9))) { str.at(ix) = static_cast<char>('0'); --ix; } if (!ix) { // There were nothing but trailing nines. if (static_cast<std::int32_t>(static_cast<std::int32_t>(str.at(ix)) - static_cast<std::int32_t>(0x30)) == static_cast<std::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]; } } else { str = "1"; ++my_exp; } } } } 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<exponent_type>(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. #ifndef BOOST_MP_STANDALONE exp = boost::lexical_cast<exponent_type>(static_cast<const char*>(str.c_str() + (pos + 1u))); #else exp = static_cast<exponent_type>(std::atoll(static_cast<const char*>(str.c_str() + (pos + 1u)))); #endif 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 = static_cast<std::string::size_type> ( static_cast<std::ptrdiff_t>(str.length()) - std::distance<std::string::const_reverse_iterator>(str.rbegin(), rit_non_zero) ); str.erase(str.begin() + static_cast<std::ptrdiff_t>(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 = static_cast<std::size_t>(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<exponent_type>(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::ptrdiff_t n_shift = static_cast<std::ptrdiff_t>(0); const std::ptrdiff_t n_exp_rem = static_cast<std::ptrdiff_t>(exp % static_cast<exponent_type>(cpp_dec_float_elem_digits10)); if((exp % static_cast<exponent_type>(cpp_dec_float_elem_digits10)) != static_cast<exponent_type>(0)) { n_shift = ((exp < static_cast<exponent_type>(0)) ? static_cast<std::ptrdiff_t>(n_exp_rem + static_cast<std::ptrdiff_t>(cpp_dec_float_elem_digits10)) : static_cast<std::ptrdiff_t>(n_exp_rem)); } // Make sure that there are enough digits for the decimal point shift. pos = str.find(static_cast<char>('.')); std::ptrdiff_t pos_plus_one = static_cast<std::ptrdiff_t>(pos + 1); if ((static_cast<std::ptrdiff_t>(str.length()) - pos_plus_one) < n_shift) { const std::ptrdiff_t sz = static_cast<std::ptrdiff_t>(n_shift - (static_cast<std::ptrdiff_t>(str.length()) - pos_plus_one)); str.append(std::string(static_cast<std::string::size_type>(sz), static_cast<char>('0'))); } // Do the decimal point shift. if (n_shift != static_cast<std::ptrdiff_t>(0)) { str.insert(static_cast<std::string::size_type>(pos_plus_one + n_shift), "."); str.erase(pos, static_cast<std::ptrdiff_t>(1)); exp -= static_cast<exponent_type>(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::ptrdiff_t>(pos + 1u); if (pos > static_cast<std::size_t>(cpp_dec_float_elem_digits10)) { const std::int32_t n_pos = static_cast<std::int32_t>(pos); const std::int32_t n_rem_is_zero = ((static_cast<std::int32_t>(n_pos % cpp_dec_float_elem_digits10) == static_cast<std::int32_t>(0)) ? static_cast<std::int32_t>(1) : static_cast<std::int32_t>(0)); const std::int32_t n = static_cast<std::int32_t>(static_cast<std::int32_t>(n_pos / cpp_dec_float_elem_digits10) - n_rem_is_zero); str.insert(static_cast<std::size_t>(static_cast<std::int32_t>(n_pos - static_cast<std::int32_t>(n * cpp_dec_float_elem_digits10))), "."); str.erase(static_cast<std::size_t>(pos_plus_one), static_cast<std::size_t>(1u)); exp += static_cast<exponent_type>(static_cast<exponent_type>(n) * static_cast<exponent_type>(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::ptrdiff_t>(pos + 1u); // Throws an error for a strange construction like 3.14L if(pos != std::string::npos && (str.back() == 'L' || str.back() == 'l' || str.back() == 'u' || str.back() == 'U')) { BOOST_MP_THROW_EXCEPTION(std::runtime_error("Can not construct a floating point with an integer literal")); } const std::int32_t n_dec = static_cast<std::int32_t>(static_cast<std::int32_t>(str.length() - 1u) - static_cast<std::int32_t>(pos)); const std::int32_t n_rem = static_cast<std::int32_t>(n_dec % cpp_dec_float_elem_digits10); std::int32_t n_cnt = ((n_rem != static_cast<std::int32_t>(0)) ? static_cast<std::int32_t>(cpp_dec_float_elem_digits10 - n_rem) : static_cast<std::int32_t>(0)); if (n_cnt != static_cast<std::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 + static_cast<std::ptrdiff_t>(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<std::uint32_t>(0u)); // Extract the data. // First get the digits to the left of the decimal point... data[0u] = static_cast<std::uint32_t>(std::stol(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 = ( static_cast<std::string::size_type>(str.length() - static_cast<std::string::size_type>(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() + static_cast<std::ptrdiff_t> ( static_cast<std::string::size_type>(pos_plus_one) + static_cast<std::string::size_type>(i * static_cast<std::string::size_type>(cpp_dec_float_elem_digits10)) ); data[i + 1u] = static_cast<std::uint32_t>(std::stol(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<exponent_type>(0); if (test.isone()) { *this = zero(); } } else { *this = zero(); } } #ifndef BOOST_NO_EXCEPTIONS } #ifndef BOOST_MP_STANDALONE catch (const bad_lexical_cast&) #else catch (const std::exception&) #endif { // 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<std::uint32_t>(0u)); return; } const bool b_neg = (mantissa < 0.0); double d = ((!b_neg) ? mantissa : -mantissa); exponent_type e = exponent; while (d > 10.0) { d /= 10.0; ++e; } while (d < 1.0) { d *= 10.0; --e; } std::int32_t shift = static_cast<std::int32_t>(e % static_cast<std::int32_t>(cpp_dec_float_elem_digits10)); while (static_cast<std::int32_t>(shift-- % cpp_dec_float_elem_digits10) != static_cast<std::int32_t>(0)) { d *= 10.0; --e; } exp = e; neg = b_neg; std::fill(data.begin(), data.end(), static_cast<std::uint32_t>(0u)); constexpr std::int32_t digit_ratio = static_cast<std::int32_t>(static_cast<std::int32_t>(std::numeric_limits<double>::digits10) / static_cast<std::int32_t>(cpp_dec_float_elem_digits10)); constexpr std::int32_t digit_loops = static_cast<std::int32_t>(digit_ratio + static_cast<std::int32_t>(2)); for (std::int32_t i = static_cast<std::int32_t>(0); i < digit_loops; i++) { std::uint32_t n = static_cast<std::uint32_t>(static_cast<std::uint64_t>(d)); data[static_cast<std::size_t>(i)] = static_cast<std::uint32_t>(n); d -= static_cast<double>(n); d *= static_cast<double>(cpp_dec_float_elem_mask); } } template <unsigned Digits10, class ExponentType, class Allocator> template <class Float> typename std::enable_if<std::is_floating_point<Float>::value, cpp_dec_float<Digits10, ExponentType, Allocator>&>::type cpp_dec_float<Digits10, ExponentType, Allocator>::operator=(Float a) { // Christopher Kormanyos's original code used a cast to long long here, but that fails // when long double has more digits than a long long. BOOST_MP_FLOAT128_USING using std::floor; using std::frexp; using std::ldexp; if (a == 0) return *this = zero(); if (a == 1) return *this = one(); if (BOOST_MP_ISINF(a)) { *this = inf(); if (a < 0) this->negate(); return *this; } if (BOOST_MP_ISNAN(a)) return *this = nan(); int e; Float 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_MP_ASSERT(!BOOST_MP_ISNAN(f) && !BOOST_MP_ISINF(f)); constexpr int shift = std::numeric_limits<int>::digits - 1; while (f != static_cast<Float>(0.0f)) { // extract int sized bits from f: f = ldexp(f, shift); BOOST_MP_ASSERT(!BOOST_MP_ISNAN(f) && !BOOST_MP_ISINF(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 unsigned long long u) { std::fill(data.begin(), data.end(), static_cast<std::uint32_t>(0u)); exp = static_cast<exponent_type>(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); unsigned long long uu = u; std::uint32_t temp[(std::numeric_limits<unsigned long long>::digits10 / static_cast<int>(cpp_dec_float_elem_digits10)) + 3] = {static_cast<std::uint32_t>(0u)}; while (uu != static_cast<unsigned long long>(0u)) { temp[i] = static_cast<std::uint32_t>(uu % static_cast<unsigned long long>(cpp_dec_float_elem_mask)); uu = static_cast<unsigned long long>(uu / static_cast<unsigned long long>(cpp_dec_float_elem_mask)); ++i; } if (i > static_cast<std::size_t>(1u)) { exp += static_cast<exponent_type>((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> template <typename InputIteratorTypeLeft, typename InputIteratorTypeRight> int cpp_dec_float<Digits10, ExponentType, Allocator>::compare_ranges(InputIteratorTypeLeft a, InputIteratorTypeRight b, const std::uint32_t count) { using local_iterator_left_type = InputIteratorTypeLeft; using local_iterator_right_type = InputIteratorTypeRight; local_iterator_left_type begin_a(a); local_iterator_left_type end_a (a + static_cast<typename std::iterator_traits<local_iterator_left_type >::difference_type>(count)); local_iterator_right_type begin_b(b); local_iterator_right_type end_b (b + static_cast<typename std::iterator_traits<local_iterator_right_type>::difference_type>(count)); const auto mismatch_pair = std::mismatch(begin_a, end_a, begin_b); int n_return; if((mismatch_pair.first != end_a) || (mismatch_pair.second != end_b)) { const typename std::iterator_traits<local_iterator_left_type >::value_type left = *mismatch_pair.first; const typename std::iterator_traits<local_iterator_right_type>::value_type right = *mismatch_pair.second; n_return = ((left > right) ? 1 : -1); } else { n_return = 0; } return n_return; } template <unsigned Digits10, class ExponentType, class Allocator> std::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::eval_add_n( std::uint32_t* r, const std::uint32_t* u, const std::uint32_t* v, const std::int32_t count) { // Addition algorithm std::uint_fast8_t carry = static_cast<std::uint_fast8_t>(0U); for(std::int32_t j = static_cast<std::int32_t>(count - static_cast<std::int32_t>(1)); j >= static_cast<std::int32_t>(0); --j) { const std::uint32_t t = static_cast<std::uint32_t>(static_cast<std::uint32_t>(u[j] + v[j]) + carry); carry = ((t >= static_cast<std::uint32_t>(cpp_dec_float_elem_mask)) ? static_cast<std::uint_fast8_t>(1U) : static_cast<std::uint_fast8_t>(0U)); r[j] = static_cast<std::uint32_t>(t - ((carry != 0U) ? static_cast<std::uint32_t>(cpp_dec_float_elem_mask) : static_cast<std::uint32_t>(0U))); } return static_cast<std::uint32_t>(carry); } template <unsigned Digits10, class ExponentType, class Allocator> std::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::eval_subtract_n( std::uint32_t* r, const std::uint32_t* u, const std::uint32_t* v, const std::int32_t count) { // Subtraction algorithm std::int_fast8_t borrow = static_cast<std::int_fast8_t>(0); for(std::uint32_t j = static_cast<std::uint32_t>(count - static_cast<std::int32_t>(1)); static_cast<std::int32_t>(j) >= static_cast<std::int32_t>(0); --j) { std::int32_t t = static_cast<std::int32_t>( static_cast<std::int32_t>(u[j]) - static_cast<std::int32_t>(v[j])) - borrow; // Underflow? Borrow? if(t < 0) { // Yes, underflow and borrow t += static_cast<std::int32_t>(cpp_dec_float_elem_mask); borrow = static_cast<std::int_fast8_t>(1); } else { borrow = static_cast<std::int_fast8_t>(0); } r[j] = static_cast<std::uint32_t>(t); } return static_cast<std::uint32_t>(borrow); } template <unsigned Digits10, class ExponentType, class Allocator> void cpp_dec_float<Digits10, ExponentType, Allocator>::eval_multiply_n_by_n_to_2n( std::uint32_t* r, const std::uint32_t* a, const std::uint32_t* b, const std::uint32_t count) { using local_limb_type = std::uint32_t; using local_double_limb_type = std::uint64_t; using local_reverse_iterator_type = std::reverse_iterator<local_limb_type*>; local_reverse_iterator_type ir(r + (count * 2)); local_double_limb_type carry = 0U; for(std::int32_t j = static_cast<std::int32_t>(count - 1); j >= static_cast<std::int32_t>(1); --j) { local_double_limb_type sum = carry; for(std::int32_t i = static_cast<std::int32_t>(count - 1); i >= j; --i) { sum += local_double_limb_type( local_double_limb_type(a[i]) * b[ static_cast<std::int32_t>(count - 1) - static_cast<std::int32_t>(i - j)]); } carry = static_cast<local_double_limb_type>(sum / static_cast<local_limb_type> (cpp_dec_float_elem_mask)); *ir++ = static_cast<local_limb_type> (sum - static_cast<local_double_limb_type>(static_cast<local_double_limb_type>(carry) * static_cast<local_limb_type>(cpp_dec_float_elem_mask))); } for(std::int32_t j = static_cast<std::int32_t>(count - 1); j >= static_cast<std::int32_t>(0); --j) { local_double_limb_type sum = carry; for(std::int32_t i = j; i >= static_cast<std::int32_t>(0); --i) { sum += static_cast<local_double_limb_type>(a[j - i] * static_cast<local_double_limb_type>(b[i])); } carry = static_cast<local_double_limb_type>(sum / static_cast<local_limb_type>(cpp_dec_float_elem_mask)); *ir++ = static_cast<local_limb_type> (sum - static_cast<local_double_limb_type>(static_cast<local_double_limb_type>(carry) * static_cast<local_limb_type>(cpp_dec_float_elem_mask))); } *ir = static_cast<local_limb_type>(carry); } template <unsigned Digits10, class ExponentType, class Allocator> std::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::mul_loop_n(std::uint32_t* const u, std::uint32_t n, const std::int32_t p) { std::uint64_t carry = static_cast<std::uint64_t>(0u); // Multiplication loop. for (std::int32_t j = p - 1; j >= static_cast<std::int32_t>(0); j--) { const std::uint64_t t = static_cast<std::uint64_t>(carry + static_cast<std::uint64_t>(u[j] * static_cast<std::uint64_t>(n))); carry = static_cast<std::uint64_t>(t / static_cast<std::uint32_t>(cpp_dec_float_elem_mask)); u[j] = static_cast<std::uint32_t>(t - static_cast<std::uint64_t>(static_cast<std::uint32_t>(cpp_dec_float_elem_mask) * static_cast<std::uint64_t>(carry))); } return static_cast<std::uint32_t>(carry); } template <unsigned Digits10, class ExponentType, class Allocator> std::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::div_loop_n(std::uint32_t* const u, std::uint32_t n, const std::int32_t p) { std::uint64_t prev = static_cast<std::uint64_t>(0u); for (std::int32_t j = static_cast<std::int32_t>(0); j < p; j++) { const std::uint64_t t = static_cast<std::uint64_t>(u[j] + static_cast<std::uint64_t>(prev * static_cast<std::uint32_t>(cpp_dec_float_elem_mask))); u[j] = static_cast<std::uint32_t>(t / n); prev = static_cast<std::uint64_t>(t - static_cast<std::uint64_t>(n * static_cast<std::uint64_t>(u[j]))); } return static_cast<std::uint32_t>(prev); } template <unsigned Digits10, class ExponentType, class Allocator> void cpp_dec_float<Digits10, ExponentType, Allocator>::eval_multiply_kara_propagate_carry(std::uint32_t* t, const std::uint32_t n, const std::uint32_t carry) { std::uint_fast8_t carry_out = ((carry != 0U) ? static_cast<std::uint_fast8_t>(1U) : static_cast<std::uint_fast8_t>(0U)); using local_reverse_iterator_type = std::reverse_iterator<std::uint32_t*>; local_reverse_iterator_type ri_t (t + n); local_reverse_iterator_type rend_t(t); while((carry_out != 0U) && (ri_t != rend_t)) { const std::uint64_t tt = *ri_t + carry_out; carry_out = ((tt >= static_cast<std::uint32_t>(cpp_dec_float_elem_mask)) ? static_cast<std::uint_fast8_t>(1U) : static_cast<std::uint_fast8_t>(0U)); *ri_t++ = static_cast<std::uint32_t>(tt - ((carry_out != 0U) ? static_cast<std::uint32_t>(cpp_dec_float_elem_mask) : static_cast<std::uint32_t>(0U))); } } template <unsigned Digits10, class ExponentType, class Allocator> void cpp_dec_float<Digits10, ExponentType, Allocator>::eval_multiply_kara_propagate_borrow(std::uint32_t* t, const std::uint32_t n, const bool has_borrow) { std::int_fast8_t borrow = (has_borrow ? static_cast<std::int_fast8_t>(1) : static_cast<std::int_fast8_t>(0)); using local_reverse_iterator_type = std::reverse_iterator<std::uint32_t*>; local_reverse_iterator_type ri_t (t + n); local_reverse_iterator_type rend_t(t); while((borrow != 0U) && (ri_t != rend_t)) { std::int32_t tt = static_cast<std::int32_t>(static_cast<std::int32_t>(*ri_t) - borrow); // Underflow? Borrow? if(tt < 0) { // Yes, underflow and borrow tt += static_cast<std::int32_t>(cpp_dec_float_elem_mask); borrow = static_cast<int_fast8_t>(1); } else { borrow = static_cast<int_fast8_t>(0); } *ri_t++ = static_cast<std::uint32_t>(tt); } } template <unsigned Digits10, class ExponentType, class Allocator> void cpp_dec_float<Digits10, ExponentType, Allocator>::eval_multiply_kara_n_by_n_to_2n( std::uint32_t* r, const std::uint32_t* a, const std::uint32_t* b, const std::uint32_t n, std::uint32_t* t) { if(n <= 32U) { static_cast<void>(t); eval_multiply_n_by_n_to_2n(r, a, b, n); } else { // Based on "Algorithm 1.3 KaratsubaMultiply", Sect. 1.3.2, page 5 // of R.P. Brent and P. Zimmermann, "Modern Computer Arithmetic", // Cambridge University Press (2011). // The Karatsuba multipliation computes the product of a*b as: // [b^N + b^(N/2)] a1*b1 + [b^(N/2)](a1 - a0)(b0 - b1) + [b^(N/2) + 1] a0*b0 // Here we visualize a and b in two components 1,0 corresponding // to the high and low order parts, respectively. // Step 1 // Calculate a1*b1 and store it in the upper-order part of r. // Calculate a0*b0 and store it in the lower-order part of r. // copy r to t0. // Step 2 // Add a1*b1 (which is t2) to the middle two-quarters of r (which is r1) // Add a0*b0 (which is t0) to the middle two-quarters of r (which is r1) // Step 3 // Calculate |a1-a0| in t0 and note the sign (i.e., the borrow flag) // Step 4 // Calculate |b0-b1| in t1 and note the sign (i.e., the borrow flag) // Step 5 // Call kara mul to calculate |a1-a0|*|b0-b1| in (t2), // while using temporary storage in t4 along the way. // Step 6 // Check the borrow signs. If a1-a0 and b0-b1 have the same signs, // then add |a1-a0|*|b0-b1| to r1, otherwise subtract it from r1. const std::uint_fast32_t nh = n / 2U; const std::uint32_t* a0 = a + nh; const std::uint32_t* a1 = a + 0U; const std::uint32_t* b0 = b + nh; const std::uint32_t* b1 = b + 0U; std::uint32_t* r0 = r + 0U; std::uint32_t* r1 = r + nh; std::uint32_t* r2 = r + n; std::uint32_t* t0 = t + 0U; std::uint32_t* t1 = t + nh; std::uint32_t* t2 = t + n; std::uint32_t* t4 = t + (n + n); // Step 1 eval_multiply_kara_n_by_n_to_2n(r0, a1, b1, static_cast<std::uint32_t>(nh), t); eval_multiply_kara_n_by_n_to_2n(r2, a0, b0, static_cast<std::uint32_t>(nh), t); std::copy(r0, r0 + (2U * n), t0); // Step 2 std::uint32_t carry; carry = eval_add_n(r1, r1, t0, static_cast<std::int32_t>(n)); eval_multiply_kara_propagate_carry(r0, static_cast<std::uint32_t>(nh), carry); carry = eval_add_n(r1, r1, t2, static_cast<std::int32_t>(n)); eval_multiply_kara_propagate_carry(r0, static_cast<std::uint32_t>(nh), carry); // Step 3 const int cmp_result_a1a0 = compare_ranges(a1, a0, static_cast<std::uint32_t>(nh)); if(cmp_result_a1a0 == 1) static_cast<void>(eval_subtract_n(t0, a1, a0, static_cast<std::int32_t>(nh))); else if(cmp_result_a1a0 == -1) static_cast<void>(eval_subtract_n(t0, a0, a1, static_cast<std::int32_t>(nh))); // Step 4 const int cmp_result_b0b1 = compare_ranges(b0, b1, static_cast<std::uint32_t>(nh)); if(cmp_result_b0b1 == 1) static_cast<void>(eval_subtract_n(t1, b0, b1, static_cast<std::int32_t>(nh))); else if(cmp_result_b0b1 == -1) static_cast<void>(eval_subtract_n(t1, b1, b0, static_cast<std::int32_t>(nh))); // Step 5 eval_multiply_kara_n_by_n_to_2n(t2, t0, t1, static_cast<std::uint32_t>(nh), t4); // Step 6 if((cmp_result_a1a0 * cmp_result_b0b1) == 1) { carry = eval_add_n(r1, r1, t2, static_cast<std::int32_t>(n)); eval_multiply_kara_propagate_carry(r0, static_cast<std::uint32_t>(nh), carry); } else if((cmp_result_a1a0 * cmp_result_b0b1) == -1) { const bool has_borrow = eval_subtract_n(r1, r1, t2, static_cast<std::int32_t>(n)); eval_multiply_kara_propagate_borrow(r0, static_cast<std::uint32_t>(nh), has_borrow); } } } template <unsigned Digits10, class ExponentType, class Allocator> cpp_dec_float<Digits10, ExponentType, Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(const long long p) { static const std::array<cpp_dec_float<Digits10, ExponentType, Allocator>, 256u> local_pow2_data = {{ cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 29u, 38735877u, 5571876u, 99218413u, 43055614u, 19454666u, 38919302u, 18803771u, 87926569u, 60431486u, 36817932u, 12890625u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 58u, 77471754u, 11143753u, 98436826u, 86111228u, 38909332u, 77838604u, 37607543u, 75853139u, 20862972u, 73635864u, 25781250u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 117u, 54943508u, 22287507u, 96873653u, 72222456u, 77818665u, 55677208u, 75215087u, 51706278u, 41725945u, 47271728u, 51562500u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 235u, 9887016u, 44575015u, 93747307u, 44444913u, 55637331u, 11354417u, 50430175u, 3412556u, 83451890u, 94543457u, 3125000u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 470u, 19774032u, 89150031u, 87494614u, 88889827u, 11274662u, 22708835u, 860350u, 6825113u, 66903781u, 89086914u, 6250000u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 940u, 39548065u, 78300063u, 74989229u, 77779654u, 22549324u, 45417670u, 1720700u, 13650227u, 33807563u, 78173828u, 12500000u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1880u, 79096131u, 56600127u, 49978459u, 55559308u, 45098648u, 90835340u, 3441400u, 27300454u, 67615127u, 56347656u, 25000000u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 3761u, 58192263u, 13200254u, 99956919u, 11118616u, 90197297u, 81670680u, 6882800u, 54600909u, 35230255u, 12695312u, 50000000u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 7523u, 16384526u, 26400509u, 99913838u, 22237233u, 80394595u, 63341360u, 13765601u, 9201818u, 70460510u, 25390625u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 15046u, 32769052u, 52801019u, 99827676u, 44474467u, 60789191u, 26682720u, 27531202u, 18403637u, 40921020u, 50781250u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 30092u, 65538105u, 5602039u, 99655352u, 88948935u, 21578382u, 53365440u, 55062404u, 36807274u, 81842041u, 1562500u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 60185u, 31076210u, 11204079u, 99310705u, 77897870u, 43156765u, 6730881u, 10124808u, 73614549u, 63684082u, 3125000u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 120370u, 62152420u, 22408159u, 98621411u, 55795740u, 86313530u, 13461762u, 20249617u, 47229099u, 27368164u, 6250000u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 240741u, 24304840u, 44816319u, 97242823u, 11591481u, 72627060u, 26923524u, 40499234u, 94458198u, 54736328u, 12500000u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 481482u, 48609680u, 89632639u, 94485646u, 23182963u, 45254120u, 53847048u, 80998469u, 88916397u, 9472656u, 25000000u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 962964u, 97219361u, 79265279u, 88971292u, 46365926u, 90508241u, 7694097u, 61996939u, 77832794u, 18945312u, 50000000u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1925929u, 94438723u, 58530559u, 77942584u, 92731853u, 81016482u, 15388195u, 23993879u, 55665588u, 37890625u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 3851859u, 88877447u, 17061119u, 55885169u, 85463707u, 62032964u, 30776390u, 47987759u, 11331176u, 75781250u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 7703719u, 77754894u, 34122239u, 11770339u, 70927415u, 24065928u, 61552780u, 95975518u, 22662353u, 51562500u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 15407439u, 55509788u, 68244478u, 23540679u, 41854830u, 48131857u, 23105561u, 91951036u, 45324707u, 3125000u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 30814879u, 11019577u, 36488956u, 47081358u, 83709660u, 96263714u, 46211123u, 83902072u, 90649414u, 6250000u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 61629758u, 22039154u, 72977912u, 94162717u, 67419321u, 92527428u, 92422247u, 67804145u, 81298828u, 12500000u }, -40 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1u, 23259516u, 44078309u, 45955825u, 88325435u, 34838643u, 85054857u, 84844495u, 35608291u, 62597656u, 25000000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 2u, 46519032u, 88156618u, 91911651u, 76650870u, 69677287u, 70109715u, 69688990u, 71216583u, 25195312u, 50000000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 4u, 93038065u, 76313237u, 83823303u, 53301741u, 39354575u, 40219431u, 39377981u, 42433166u, 50390625u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 9u, 86076131u, 52626475u, 67646607u, 6603482u, 78709150u, 80438862u, 78755962u, 84866333u, 781250u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 19u, 72152263u, 5252951u, 35293214u, 13206965u, 57418301u, 60877725u, 57511925u, 69732666u, 1562500u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 39u, 44304526u, 10505902u, 70586428u, 26413931u, 14836603u, 21755451u, 15023851u, 39465332u, 3125000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 78u, 88609052u, 21011805u, 41172856u, 52827862u, 29673206u, 43510902u, 30047702u, 78930664u, 6250000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 157u, 77218104u, 42023610u, 82345713u, 5655724u, 59346412u, 87021804u, 60095405u, 57861328u, 12500000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 315u, 54436208u, 84047221u, 64691426u, 11311449u, 18692825u, 74043609u, 20190811u, 15722656u, 25000000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 631u, 8872417u, 68094443u, 29382852u, 22622898u, 37385651u, 48087218u, 40381622u, 31445312u, 50000000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1262u, 17744835u, 36188886u, 58765704u, 45245796u, 74771302u, 96174436u, 80763244u, 62890625u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 2524u, 35489670u, 72377773u, 17531408u, 90491593u, 49542605u, 92348873u, 61526489u, 25781250u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 5048u, 70979341u, 44755546u, 35062817u, 80983186u, 99085211u, 84697747u, 23052978u, 51562500u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 10097u, 41958682u, 89511092u, 70125635u, 61966373u, 98170423u, 69395494u, 46105957u, 3125000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 20194u, 83917365u, 79022185u, 40251271u, 23932747u, 96340847u, 38790988u, 92211914u, 6250000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 40389u, 67834731u, 58044370u, 80502542u, 47865495u, 92681694u, 77581977u, 84423828u, 12500000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 80779u, 35669463u, 16088741u, 61005084u, 95730991u, 85363389u, 55163955u, 68847656u, 25000000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 161558u, 71338926u, 32177483u, 22010169u, 91461983u, 70726779u, 10327911u, 37695312u, 50000000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 323117u, 42677852u, 64354966u, 44020339u, 82923967u, 41453558u, 20655822u, 75390625u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 646234u, 85355705u, 28709932u, 88040679u, 65847934u, 82907116u, 41311645u, 50781250u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1292469u, 70711410u, 57419865u, 76081359u, 31695869u, 65814232u, 82623291u, 1562500u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 2584939u, 41422821u, 14839731u, 52162718u, 63391739u, 31628465u, 65246582u, 3125000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 5169878u, 82845642u, 29679463u, 4325437u, 26783478u, 63256931u, 30493164u, 6250000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 10339757u, 65691284u, 59358926u, 8650874u, 53566957u, 26513862u, 60986328u, 12500000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 20679515u, 31382569u, 18717852u, 17301749u, 7133914u, 53027725u, 21972656u, 25000000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 41359030u, 62765138u, 37435704u, 34603498u, 14267829u, 6055450u, 43945312u, 50000000u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 82718061u, 25530276u, 74871408u, 69206996u, 28535658u, 12110900u, 87890625u }, -32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1u, 65436122u, 51060553u, 49742817u, 38413992u, 57071316u, 24221801u, 75781250u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 3u, 30872245u, 2121106u, 99485634u, 76827985u, 14142632u, 48443603u, 51562500u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 6u, 61744490u, 4242213u, 98971269u, 53655970u, 28285264u, 96887207u, 3125000u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 13u, 23488980u, 8484427u, 97942539u, 7311940u, 56570529u, 93774414u, 6250000u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 26u, 46977960u, 16968855u, 95885078u, 14623881u, 13141059u, 87548828u, 12500000u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 52u, 93955920u, 33937711u, 91770156u, 29247762u, 26282119u, 75097656u, 25000000u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 105u, 87911840u, 67875423u, 83540312u, 58495524u, 52564239u, 50195312u, 50000000u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 211u, 75823681u, 35750847u, 67080625u, 16991049u, 5128479u, 390625u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 423u, 51647362u, 71501695u, 34161250u, 33982098u, 10256958u, 781250u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 847u, 3294725u, 43003390u, 68322500u, 67964196u, 20513916u, 1562500u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1694u, 6589450u, 86006781u, 36645001u, 35928392u, 41027832u, 3125000u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 3388u, 13178901u, 72013562u, 73290002u, 71856784u, 82055664u, 6250000u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 6776u, 26357803u, 44027125u, 46580005u, 43713569u, 64111328u, 12500000u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 13552u, 52715606u, 88054250u, 93160010u, 87427139u, 28222656u, 25000000u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 27105u, 5431213u, 76108501u, 86320021u, 74854278u, 56445312u, 50000000u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 54210u, 10862427u, 52217003u, 72640043u, 49708557u, 12890625u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 108420u, 21724855u, 4434007u, 45280086u, 99417114u, 25781250u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 216840u, 43449710u, 8868014u, 90560173u, 98834228u, 51562500u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 433680u, 86899420u, 17736029u, 81120347u, 97668457u, 3125000u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 867361u, 73798840u, 35472059u, 62240695u, 95336914u, 6250000u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1734723u, 47597680u, 70944119u, 24481391u, 90673828u, 12500000u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 3469446u, 95195361u, 41888238u, 48962783u, 81347656u, 25000000u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 6938893u, 90390722u, 83776476u, 97925567u, 62695312u, 50000000u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 13877787u, 80781445u, 67552953u, 95851135u, 25390625u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 27755575u, 61562891u, 35105907u, 91702270u, 50781250u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 55511151u, 23125782u, 70211815u, 83404541u, 1562500u }, -24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1u, 11022302u, 46251565u, 40423631u, 66809082u, 3125000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 2u, 22044604u, 92503130u, 80847263u, 33618164u, 6250000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 4u, 44089209u, 85006261u, 61694526u, 67236328u, 12500000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 8u, 88178419u, 70012523u, 23389053u, 34472656u, 25000000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 17u, 76356839u, 40025046u, 46778106u, 68945312u, 50000000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 35u, 52713678u, 80050092u, 93556213u, 37890625u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 71u, 5427357u, 60100185u, 87112426u, 75781250u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 142u, 10854715u, 20200371u, 74224853u, 51562500u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 284u, 21709430u, 40400743u, 48449707u, 3125000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 568u, 43418860u, 80801486u, 96899414u, 6250000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1136u, 86837721u, 61602973u, 93798828u, 12500000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 2273u, 73675443u, 23205947u, 87597656u, 25000000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 4547u, 47350886u, 46411895u, 75195312u, 50000000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 9094u, 94701772u, 92823791u, 50390625u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 18189u, 89403545u, 85647583u, 781250u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 36379u, 78807091u, 71295166u, 1562500u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 72759u, 57614183u, 42590332u, 3125000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 145519u, 15228366u, 85180664u, 6250000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 291038u, 30456733u, 70361328u, 12500000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 582076u, 60913467u, 40722656u, 25000000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1164153u, 21826934u, 81445312u, 50000000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 2328306u, 43653869u, 62890625u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 4656612u, 87307739u, 25781250u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 9313225u, 74615478u, 51562500u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 18626451u, 49230957u, 3125000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 37252902u, 98461914u, 6250000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 74505805u, 96923828u, 12500000u }, -16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1u, 49011611u, 93847656u, 25000000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 2u, 98023223u, 87695312u, 50000000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 5u, 96046447u, 75390625u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 11u, 92092895u, 50781250u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 23u, 84185791u, 1562500u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 47u, 68371582u, 3125000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 95u, 36743164u, 6250000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 190u, 73486328u, 12500000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 381u, 46972656u, 25000000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 762u, 93945312u, 50000000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1525u, 87890625u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 3051u, 75781250u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 6103u, 51562500u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 12207u, 3125000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 24414u, 6250000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 48828u, 12500000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 97656u, 25000000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 195312u, 50000000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 390625u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 781250u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1562500u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 3125000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 6250000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 12500000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 25000000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 50000000u }, -8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 2u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 4u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 8u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 16u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 32u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 64u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 128u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 256u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 512u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1024u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 2048u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 4096u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 8192u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 16384u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 32768u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 65536u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 131072u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 262144u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 524288u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1048576u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 2097152u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 4194304u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 8388608u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 16777216u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 33554432u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 67108864u }, 0 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1u, 34217728u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 2u, 68435456u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 5u, 36870912u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 10u, 73741824u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 21u, 47483648u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 42u, 94967296u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 85u, 89934592u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 171u, 79869184u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 343u, 59738368u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 687u, 19476736u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1374u, 38953472u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 2748u, 77906944u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 5497u, 55813888u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 10995u, 11627776u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 21990u, 23255552u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 43980u, 46511104u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 87960u, 93022208u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 175921u, 86044416u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 351843u, 72088832u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 703687u, 44177664u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1407374u, 88355328u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 2814749u, 76710656u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 5629499u, 53421312u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 11258999u, 6842624u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 22517998u, 13685248u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 45035996u, 27370496u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 90071992u, 54740992u }, 8 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1u, 80143985u, 9481984u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 3u, 60287970u, 18963968u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 7u, 20575940u, 37927936u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 14u, 41151880u, 75855872u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 28u, 82303761u, 51711744u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 57u, 64607523u, 3423488u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 115u, 29215046u, 6846976u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 230u, 58430092u, 13693952u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 461u, 16860184u, 27387904u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 922u, 33720368u, 54775808u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1844u, 67440737u, 9551616u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 3689u, 34881474u, 19103232u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 7378u, 69762948u, 38206464u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 14757u, 39525896u, 76412928u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 29514u, 79051793u, 52825856u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 59029u, 58103587u, 5651712u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 118059u, 16207174u, 11303424u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 236118u, 32414348u, 22606848u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 472236u, 64828696u, 45213696u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 944473u, 29657392u, 90427392u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1888946u, 59314785u, 80854784u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 3777893u, 18629571u, 61709568u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 7555786u, 37259143u, 23419136u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 15111572u, 74518286u, 46838272u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 30223145u, 49036572u, 93676544u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 60446290u, 98073145u, 87353088u }, 16 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1u, 20892581u, 96146291u, 74706176u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 2u, 41785163u, 92292583u, 49412352u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 4u, 83570327u, 84585166u, 98824704u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 9u, 67140655u, 69170333u, 97649408u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 19u, 34281311u, 38340667u, 95298816u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 38u, 68562622u, 76681335u, 90597632u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 77u, 37125245u, 53362671u, 81195264u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 154u, 74250491u, 6725343u, 62390528u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 309u, 48500982u, 13450687u, 24781056u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 618u, 97001964u, 26901374u, 49562112u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1237u, 94003928u, 53802748u, 99124224u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 2475u, 88007857u, 7605497u, 98248448u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 4951u, 76015714u, 15210995u, 96496896u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 9903u, 52031428u, 30421991u, 92993792u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 19807u, 4062856u, 60843983u, 85987584u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 39614u, 8125713u, 21687967u, 71975168u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 79228u, 16251426u, 43375935u, 43950336u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 158456u, 32502852u, 86751870u, 87900672u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 316912u, 65005705u, 73503741u, 75801344u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 633825u, 30011411u, 47007483u, 51602688u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1267650u, 60022822u, 94014967u, 3205376u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 2535301u, 20045645u, 88029934u, 6410752u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 5070602u, 40091291u, 76059868u, 12821504u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 10141204u, 80182583u, 52119736u, 25643008u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 20282409u, 60365167u, 4239472u, 51286016u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 40564819u, 20730334u, 8478945u, 2572032u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 81129638u, 41460668u, 16957890u, 5144064u }, 24 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1u, 62259276u, 82921336u, 33915780u, 10288128u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 3u, 24518553u, 65842672u, 67831560u, 20576256u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 6u, 49037107u, 31685345u, 35663120u, 41152512u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 12u, 98074214u, 63370690u, 71326240u, 82305024u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 25u, 96148429u, 26741381u, 42652481u, 64610048u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 51u, 92296858u, 53482762u, 85304963u, 29220096u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 103u, 84593717u, 6965525u, 70609926u, 58440192u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 207u, 69187434u, 13931051u, 41219853u, 16880384u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 415u, 38374868u, 27862102u, 82439706u, 33760768u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 830u, 76749736u, 55724205u, 64879412u, 67521536u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1661u, 53499473u, 11448411u, 29758825u, 35043072u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 3323u, 6998946u, 22896822u, 59517650u, 70086144u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 6646u, 13997892u, 45793645u, 19035301u, 40172288u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 13292u, 27995784u, 91587290u, 38070602u, 80344576u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 26584u, 55991569u, 83174580u, 76141205u, 60689152u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 53169u, 11983139u, 66349161u, 52282411u, 21378304u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 106338u, 23966279u, 32698323u, 4564822u, 42756608u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 212676u, 47932558u, 65396646u, 9129644u, 85513216u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 425352u, 95865117u, 30793292u, 18259289u, 71026432u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 850705u, 91730234u, 61586584u, 36518579u, 42052864u }, 32 ), cpp_dec_float<Digits10, ExponentType, Allocator>::from_lst( { 1701411u, 83460469u, 23173168u, 73037158u, 84105728u }, 32 ), }}; cpp_dec_float<Digits10, ExponentType, Allocator> t; if(p < -128L) default_ops::detail::pow_imp(t, cpp_dec_float<Digits10, ExponentType, Allocator>::half(), static_cast<unsigned long long>(-p), std::integral_constant<bool, false>()); else if ((p >= -128L) && (p <= 127L)) t = local_pow2_data[std::size_t(p + 128)]; else default_ops::detail::pow_imp(t, cpp_dec_float<Digits10, ExponentType, Allocator>::two(), static_cast<unsigned long long>(p), std::integral_constant<bool, false>()); 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 unsigned long long& 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 unsigned long long& 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 unsigned long long& 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 unsigned long long& 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, long long o) { if (o < 0) result.sub_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o)); else { using local_ulonglong_type = typename boost::multiprecision::detail::make_unsigned<long long>::type; result.add_unsigned_long_long(static_cast<local_ulonglong_type>(o)); } } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, long long o) { if (o < 0) result.add_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o)); else { using local_ulonglong_type = typename boost::multiprecision::detail::make_unsigned<long long>::type; result.sub_unsigned_long_long(static_cast<local_ulonglong_type>(o)); } } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, long long o) { if (o < 0) { result.mul_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o)); result.negate(); } else { using local_ulonglong_type = typename boost::multiprecision::detail::make_unsigned<long long>::type; result.mul_unsigned_long_long(static_cast<local_ulonglong_type>(o)); } } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, long long o) { if (o < 0) { result.div_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o)); result.negate(); } else { using local_ulonglong_type = typename boost::multiprecision::detail::make_unsigned<long long>::type; result.div_unsigned_long_long(static_cast<local_ulonglong_type>(o)); } } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_convert_to(unsigned long long* 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(long long* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val) { *result = val.extract_signed_long_long(); } #ifdef BOOST_HAS_INT128 template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_convert_to(uint128_type* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val) { *result = val.extract_unsigned_int128(); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_convert_to(int128_type* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val) { *result = val.extract_signed_int128(); } #endif template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_convert_to(long double* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val) { *result = val.extract_long_double(); } template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_convert_to(double* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val) { *result = val.extract_double(); } #if defined(BOOST_HAS_FLOAT128) template <unsigned Digits10, class ExponentType, class Allocator> inline void eval_convert_to(float128_type* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val) { *result = float128_procs::strtoflt128(val.str(0, std::ios_base::scientific).c_str(), nullptr); } #endif // // 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<typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type>::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 typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type e = static_cast<typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type>(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 long long the_exp = static_cast<long long>(e); if ((the_exp > (std::numeric_limits<typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type>::max)()) || (the_exp < (std::numeric_limits<typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type>::min)())) BOOST_MP_THROW_EXCEPTION(std::runtime_error(std::string("Exponent value is out of range."))); result = x; if ((the_exp > static_cast<long long>(-std::numeric_limits<long long>::digits)) && (the_exp < static_cast<long long>(0))) result.div_unsigned_long_long(1ULL << static_cast<long long>(-the_exp)); else if ((the_exp < static_cast<long long>(std::numeric_limits<long long>::digits)) && (the_exp > static_cast<long long>(0))) result.mul_unsigned_long_long(1ULL << the_exp); else if (the_exp != static_cast<long long>(0)) { if ((the_exp < cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp / 2) && (x.order() > 0)) { long long half_exp = e / 2; cpp_dec_float<Digits10, ExponentType, Allocator> t = cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(half_exp); result *= t; if (2 * half_exp != e) t *= 2; result *= t; } else 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(); typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type t = result.order(); BOOST_MP_USING_ABS if (abs(t) < ((std::numeric_limits<typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type>::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: typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type e2; cpp_dec_float<Digits10, ExponentType, Allocator> r2; eval_frexp(r2, result, &e2); // overflow protection: if ((t > 0) && (e2 > 0) && (t > (std::numeric_limits<typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type>::max)() - e2)) BOOST_MP_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<typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type>::min)() - e2)) BOOST_MP_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 std::enable_if< !std::is_same<ExponentType, int>::value>::type eval_frexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, int* e) { typename cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type t; eval_frexp(result, x, &t); if ((t > (std::numeric_limits<int>::max)()) || (t < (std::numeric_limits<int>::min)())) BOOST_MP_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; using cpp_dec_float_50 = number<cpp_dec_float<50> > ; using cpp_dec_float_100 = number<cpp_dec_float<100> >; namespace detail { template <unsigned Digits10, class ExponentType, class Allocator> struct transcendental_reduction_type<boost::multiprecision::backends::cpp_dec_float<Digits10, ExponentType, Allocator> > { // // The type used for trigonometric reduction needs 3 times the precision of the base type. // This is double the precision of the original type, plus the largest exponent supported. // As a practical measure the largest argument supported is 1/eps, as supporting larger // arguments requires the division of argument by PI/2 to also be done at higher precision, // otherwise the result (an integer) can not be represented exactly. // // See ARGUMENT REDUCTION FOR HUGE ARGUMENTS. K C Ng. // using type = boost::multiprecision::backends::cpp_dec_float<Digits10 * 3, ExponentType, Allocator>; }; } // namespace detail }} // 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: static constexpr bool is_specialized = true; static constexpr bool is_signed = true; static constexpr bool is_integer = false; static constexpr bool is_exact = false; static constexpr bool is_bounded = true; static constexpr bool is_modulo = false; static constexpr bool is_iec559 = false; static constexpr int digits = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10; static constexpr int digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10; static constexpr int max_digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_digits10; static constexpr typename boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type min_exponent = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp; // Type differs from int. static constexpr typename boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type min_exponent10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10; // Type differs from int. static constexpr typename boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type max_exponent = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp; // Type differs from int. static constexpr typename boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type max_exponent10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10; // Type differs from int. static constexpr int radix = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_radix; static constexpr std::float_round_style round_style = std::round_indeterminate; static constexpr bool has_infinity = true; static constexpr bool has_quiet_NaN = true; static constexpr bool has_signaling_NaN = false; static constexpr std::float_denorm_style has_denorm = std::denorm_absent; static constexpr bool has_denorm_loss = false; static constexpr bool traps = false; static constexpr bool tinyness_before = false; 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)(); } 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)(); } 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(); } 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(); } static constexpr boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> round_error() { return 0.5L; } 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(); } 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(); } 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(); } 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(); } }; template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> constexpr 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> constexpr 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> constexpr 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> constexpr 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> constexpr 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> constexpr 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> constexpr 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> constexpr typename boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type 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> constexpr typename boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type 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> constexpr typename boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type 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> constexpr typename boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::exponent_type 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> constexpr 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> constexpr 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> constexpr 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> constexpr 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> constexpr 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> constexpr 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> constexpr 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> constexpr 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> constexpr 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> constexpr 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> constexpr float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::round_style; } // namespace std #ifdef BOOST_MP_MATH_AVAILABLE 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 constexpr std::int32_t cpp_dec_float_digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10; using precision_type = typename Policy::precision_type ; using digits_2 = digits2<((cpp_dec_float_digits10 + 1LL) * 1000LL) / 301LL>; using type = typename std::conditional< ((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; }; } }} // namespace boost::math::policies #endif #ifdef BOOST_MSVC #pragma warning(pop) #endif #endif