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libcarla/include/system/boost/multiprecision/cpp_dec_float.hpp

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2024-10-18 13:19:59 +08:00
///////////////////////////////////////////////////////////////////////////////
// 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
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