ceph/src/boost/boost/multiprecision/cpp_dec_float.hpp

   1 ///////////////////////////////////////////////////////////////////////////////
   2 // Copyright Christopher Kormanyos 2002 - 2013.
   3 // Copyright 2011 -2013 John Maddock. Distributed under the Boost
   4 // Software License, Version 1.0. (See accompanying file
   5 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   6 //
   7 // This work is based on an earlier work:
   8 // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
   9 // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
  10 //
  11 // Note that there are no "noexcept" specifications on the functions in this file: there are too many
  12 // calls to lexical_cast (and similar) to easily analyse the code for correctness. So until compilers
  13 // can detect noexcept misuse at compile time, the only realistic option is to simply not use it here.
  14 //
  15
  16 #ifndef BOOST_MP_CPP_DEC_FLOAT_BACKEND_HPP
  17 #define BOOST_MP_CPP_DEC_FLOAT_BACKEND_HPP
  18
  19 #include <boost/config.hpp>
  20 #include <boost/cstdint.hpp>
  21 #include <limits>
  22 #ifndef BOOST_NO_CXX11_HDR_ARRAY
  23 #include <array>
  24 #else
  25 #include <boost/array.hpp>
  26 #endif
  27 #include <boost/cstdint.hpp>
  28 #include <boost/functional/hash_fwd.hpp>
  29 #include <boost/multiprecision/number.hpp>
  30 #include <boost/multiprecision/detail/big_lanczos.hpp>
  31 #include <boost/multiprecision/detail/dynamic_array.hpp>
  32
  33 //
  34 // Headers required for Boost.Math integration:
  35 //
  36 #include <boost/math/policies/policy.hpp>
  37 //
  38 // Some includes we need from Boost.Math, since we rely on that library to provide these functions:
  39 //
  40 #include <boost/math/special_functions/asinh.hpp>
  41 #include <boost/math/special_functions/acosh.hpp>
  42 #include <boost/math/special_functions/atanh.hpp>
  43 #include <boost/math/special_functions/cbrt.hpp>
  44 #include <boost/math/special_functions/expm1.hpp>
  45 #include <boost/math/special_functions/gamma.hpp>
  46
  47 #ifdef BOOST_MSVC
  48 #pragma warning(push)
  49 #pragma warning(disable:6326)  // comparison of two constants
  50 #endif
  51
  52 namespace boost{
  53 namespace multiprecision{
  54 namespace backends{
  55
  56 template <unsigned Digits10, class ExponentType = boost::int32_t, class Allocator = void>
  57 class cpp_dec_float;
  58
  59 } // namespace
  60
  61 template <unsigned Digits10, class ExponentType, class Allocator>
  62 struct number_category<backends::cpp_dec_float<Digits10, ExponentType, Allocator> > : public mpl::int_<number_kind_floating_point>{};
  63
  64 namespace backends{
  65
  66 template <unsigned Digits10, class ExponentType, class Allocator>
  67 class cpp_dec_float
  68 {
  69 private:
  70    static const boost::int32_t cpp_dec_float_digits10_setting = Digits10;
  71
  72    // We need at least 16-bits in the exponent type to do anything sensible:
  73    BOOST_STATIC_ASSERT_MSG(boost::is_signed<ExponentType>::value, "ExponentType must be a signed built in integer type.");
  74    BOOST_STATIC_ASSERT_MSG(sizeof(ExponentType) > 1, "ExponentType is too small.");
  75
  76 public:
  77    typedef mpl::list<boost::long_long_type> signed_types;
  78    typedef mpl::list<boost::ulong_long_type> unsigned_types;
  79    typedef mpl::list<long double> float_types;
  80    typedef ExponentType exponent_type;
  81
  82    static const boost::int32_t cpp_dec_float_radix = 10L;
  83    static const boost::int32_t cpp_dec_float_digits10_limit_lo = 9L;
  84    static const boost::int32_t cpp_dec_float_digits10_limit_hi = boost::integer_traits<boost::int32_t>::const_max - 100;
  85    static const boost::int32_t cpp_dec_float_digits10 = ((cpp_dec_float_digits10_setting < cpp_dec_float_digits10_limit_lo) ? cpp_dec_float_digits10_limit_lo : ((cpp_dec_float_digits10_setting > cpp_dec_float_digits10_limit_hi) ? cpp_dec_float_digits10_limit_hi : cpp_dec_float_digits10_setting));
  86    static const ExponentType cpp_dec_float_max_exp10 = (static_cast<ExponentType>(1) << (std::numeric_limits<ExponentType>::digits - 5));
  87    static const ExponentType cpp_dec_float_min_exp10 = -cpp_dec_float_max_exp10;
  88    static const ExponentType cpp_dec_float_max_exp = cpp_dec_float_max_exp10;
  89    static const ExponentType cpp_dec_float_min_exp = cpp_dec_float_min_exp10;
  90
  91    BOOST_STATIC_ASSERT((cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10 == -cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10));
  92
  93 private:
  94    static const boost::int32_t cpp_dec_float_elem_digits10 = 8L;
  95    static const boost::int32_t cpp_dec_float_elem_mask = 100000000L;
  96
  97    BOOST_STATIC_ASSERT(0 == cpp_dec_float_max_exp10 % cpp_dec_float_elem_digits10);
  98
  99    // There are three guard limbs.
 100    // 1) The first limb has 'play' from 1...8 decimal digits.
 101    // 2) The last limb also has 'play' from 1...8 decimal digits.
 102    // 3) One limb can get lost when justifying after multiply,
 103    // as only half of the triangle is multiplied and a carry
 104    // from below is missing.
 105    static const boost::int32_t cpp_dec_float_elem_number_request = static_cast<boost::int32_t>((cpp_dec_float_digits10 / cpp_dec_float_elem_digits10) + (((cpp_dec_float_digits10 % cpp_dec_float_elem_digits10) != 0) ? 1 : 0));
 106
 107    // The number of elements needed (with a minimum of two) plus three added guard limbs.
 108    static const boost::int32_t cpp_dec_float_elem_number = static_cast<boost::int32_t>(((cpp_dec_float_elem_number_request < 2L) ? 2L : cpp_dec_float_elem_number_request) + 3L);
 109
 110 public:
 111    static const boost::int32_t cpp_dec_float_total_digits10 = static_cast<boost::int32_t>(cpp_dec_float_elem_number * cpp_dec_float_elem_digits10);
 112
 113 private:
 114
 115    typedef enum enum_fpclass_type
 116    {
 117       cpp_dec_float_finite,
 118       cpp_dec_float_inf,
 119       cpp_dec_float_NaN
 120    }
 121    fpclass_type;
 122
 123 #ifndef BOOST_NO_CXX11_HDR_ARRAY
 124    typedef typename mpl::if_<is_void<Allocator>,
 125       std::array<boost::uint32_t, cpp_dec_float_elem_number>,
 126       detail::dynamic_array<boost::uint32_t, cpp_dec_float_elem_number, Allocator>
 127       >::type array_type;
 128 #else
 129    typedef typename mpl::if_<is_void<Allocator>,
 130       boost::array<boost::uint32_t, cpp_dec_float_elem_number>,
 131       detail::dynamic_array<boost::uint32_t, cpp_dec_float_elem_number, Allocator>
 132       >::type array_type;
 133 #endif
 134
 135    array_type data;
 136    ExponentType exp;
 137    bool neg;
 138    fpclass_type fpclass;
 139    boost::int32_t prec_elem;
 140
 141    //
 142    // Special values constructor:
 143    //
 144    cpp_dec_float(fpclass_type c) :
 145       data(),
 146       exp (static_cast<ExponentType>(0)),
 147       neg (false),
 148       fpclass (c),
 149       prec_elem(cpp_dec_float_elem_number) { }
 150
 151       //
 152       // Static data initializer:
 153       //
 154       struct initializer
 155       {
 156          initializer()
 157          {
 158              cpp_dec_float<Digits10, ExponentType, Allocator>::nan();
 159              cpp_dec_float<Digits10, ExponentType, Allocator>::inf();
 160             (cpp_dec_float<Digits10, ExponentType, Allocator>::min)();
 161             (cpp_dec_float<Digits10, ExponentType, Allocator>::max)();
 162              cpp_dec_float<Digits10, ExponentType, Allocator>::zero();
 163              cpp_dec_float<Digits10, ExponentType, Allocator>::one();
 164              cpp_dec_float<Digits10, ExponentType, Allocator>::two();
 165              cpp_dec_float<Digits10, ExponentType, Allocator>::half();
 166              cpp_dec_float<Digits10, ExponentType, Allocator>::double_min();
 167              cpp_dec_float<Digits10, ExponentType, Allocator>::double_max();
 168              cpp_dec_float<Digits10, ExponentType, Allocator>::long_double_max();
 169              cpp_dec_float<Digits10, ExponentType, Allocator>::long_double_min();
 170              cpp_dec_float<Digits10, ExponentType, Allocator>::long_long_max();
 171              cpp_dec_float<Digits10, ExponentType, Allocator>::long_long_min();
 172              cpp_dec_float<Digits10, ExponentType, Allocator>::ulong_long_max();
 173              cpp_dec_float<Digits10, ExponentType, Allocator>::eps();
 174              cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(0);
 175          }
 176          void do_nothing(){}
 177       };
 178
 179       static initializer init;
 180
 181 public:
 182    // Constructors
 183    cpp_dec_float() BOOST_MP_NOEXCEPT_IF(noexcept(array_type())) :
 184       data(),
 185       exp (static_cast<ExponentType>(0)),
 186       neg (false),
 187       fpclass (cpp_dec_float_finite),
 188       prec_elem(cpp_dec_float_elem_number) { }
 189
 190    cpp_dec_float(const char* s) :
 191       data(),
 192       exp (static_cast<ExponentType>(0)),
 193       neg (false),
 194       fpclass (cpp_dec_float_finite),
 195       prec_elem(cpp_dec_float_elem_number)
 196       {
 197          *this = s;
 198       }
 199
 200    template<class I>
 201    cpp_dec_float(I i, typename enable_if<is_unsigned<I> >::type* = 0) :
 202       data(),
 203       exp (static_cast<ExponentType>(0)),
 204       neg (false),
 205       fpclass (cpp_dec_float_finite),
 206       prec_elem(cpp_dec_float_elem_number)
 207       {
 208          from_unsigned_long_long(i);
 209       }
 210
 211    template <class I>
 212    cpp_dec_float(I i, typename enable_if<is_signed<I> >::type* = 0) :
 213       data(),
 214       exp (static_cast<ExponentType>(0)),
 215       neg (false),
 216       fpclass (cpp_dec_float_finite),
 217       prec_elem(cpp_dec_float_elem_number)
 218       {
 219          if(i < 0)
 220          {
 221             from_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(i));
 222             negate();
 223          }
 224          else
 225             from_unsigned_long_long(i);
 226       }
 227
 228    cpp_dec_float(const cpp_dec_float& f) BOOST_MP_NOEXCEPT_IF(noexcept(array_type(std::declval<const array_type&>()))) :
 229       data (f.data),
 230       exp (f.exp),
 231       neg (f.neg),
 232       fpclass (f.fpclass),
 233       prec_elem(f.prec_elem) { }
 234
 235    template <unsigned D, class ET, class A>
 236    cpp_dec_float(const cpp_dec_float<D, ET, A>& f, typename enable_if_c<D <= Digits10>::type* = 0) :
 237       data(),
 238       exp (f.exp),
 239       neg (f.neg),
 240       fpclass (static_cast<fpclass_type>(static_cast<int>(f.fpclass))),
 241       prec_elem(cpp_dec_float_elem_number)
 242    {
 243       std::copy(f.data.begin(), f.data.begin() + f.prec_elem, data.begin());
 244    }
 245    template <unsigned D, class ET, class A>
 246    explicit cpp_dec_float(const cpp_dec_float<D, ET, A>& f, typename disable_if_c<D <= Digits10>::type* = 0) :
 247       data(),
 248       exp (f.exp),
 249       neg (f.neg),
 250       fpclass (static_cast<fpclass_type>(static_cast<int>(f.fpclass))),
 251       prec_elem(cpp_dec_float_elem_number)
 252    {
 253       // TODO: this doesn't round!
 254       std::copy(f.data.begin(), f.data.begin() + prec_elem, data.begin());
 255    }
 256
 257    template <class F>
 258    cpp_dec_float(const F val, typename enable_if_c<is_floating_point<F>::value
 259 #ifdef BOOST_HAS_FLOAT128
 260       && !boost::is_same<F, __float128>::value
 261 #endif
 262    >::type* = 0) :
 263       data(),
 264       exp (static_cast<ExponentType>(0)),
 265       neg (false),
 266       fpclass (cpp_dec_float_finite),
 267       prec_elem(cpp_dec_float_elem_number)
 268    {
 269       *this = val;
 270    }
 271
 272    cpp_dec_float(const double mantissa, const ExponentType exponent);
 273
 274    std::size_t hash()const
 275    {
 276       std::size_t result = 0;
 277       for(int i = 0; i < prec_elem; ++i)
 278          boost::hash_combine(result, data[i]);
 279       boost::hash_combine(result, exp);
 280       boost::hash_combine(result, neg);
 281       boost::hash_combine(result, fpclass);
 282       return result;
 283    }
 284
 285    // Specific special values.
 286    static const cpp_dec_float& nan()
 287    {
 288       static const cpp_dec_float val(cpp_dec_float_NaN);
 289       init.do_nothing();
 290       return val;
 291    }
 292
 293    static const cpp_dec_float& inf()
 294    {
 295       static const cpp_dec_float val(cpp_dec_float_inf);
 296       init.do_nothing();
 297       return val;
 298    }
 299
 300    static const cpp_dec_float& (max)()
 301    {
 302       init.do_nothing();
 303       static cpp_dec_float val_max = std::string("1.0e" + boost::lexical_cast<std::string>(cpp_dec_float_max_exp10)).c_str();
 304       return val_max;
 305    }
 306
 307    static const cpp_dec_float& (min)()
 308    {
 309       init.do_nothing();
 310       static cpp_dec_float val_min = std::string("1.0e" + boost::lexical_cast<std::string>(cpp_dec_float_min_exp10)).c_str();
 311       return val_min;
 312    }
 313
 314    static const cpp_dec_float& zero()
 315    {
 316       init.do_nothing();
 317       static cpp_dec_float val(static_cast<boost::ulong_long_type>(0u));
 318       return val;
 319    }
 320
 321    static const cpp_dec_float& one()
 322    {
 323       init.do_nothing();
 324       static cpp_dec_float val(static_cast<boost::ulong_long_type>(1u));
 325       return val;
 326    }
 327
 328    static const cpp_dec_float& two()
 329    {
 330       init.do_nothing();
 331       static cpp_dec_float val(static_cast<boost::ulong_long_type>(2u));
 332       return val;
 333    }
 334
 335    static const cpp_dec_float& half()
 336    {
 337       init.do_nothing();
 338       static cpp_dec_float val(0.5L);
 339       return val;
 340    }
 341
 342    static const cpp_dec_float& double_min()
 343    {
 344       init.do_nothing();
 345       static cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::min)()));
 346       return val;
 347    }
 348
 349    static const cpp_dec_float& double_max()
 350    {
 351       init.do_nothing();
 352       static cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::max)()));
 353       return val;
 354    }
 355
 356    static const cpp_dec_float& long_double_min()
 357    {
 358       init.do_nothing();
 359 #ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 360       static cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::min)()));
 361 #else
 362       static cpp_dec_float val((std::numeric_limits<long double>::min)());
 363 #endif
 364       return val;
 365    }
 366
 367    static const cpp_dec_float& long_double_max()
 368    {
 369       init.do_nothing();
 370 #ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 371       static cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::max)()));
 372 #else
 373       static cpp_dec_float val((std::numeric_limits<long double>::max)());
 374 #endif
 375       return val;
 376    }
 377
 378    static const cpp_dec_float& long_long_max()
 379    {
 380       init.do_nothing();
 381       static cpp_dec_float val((std::numeric_limits<boost::long_long_type>::max)());
 382       return val;
 383    }
 384
 385    static const cpp_dec_float& long_long_min()
 386    {
 387       init.do_nothing();
 388       static cpp_dec_float val((std::numeric_limits<boost::long_long_type>::min)());
 389       return val;
 390    }
 391
 392    static const cpp_dec_float& ulong_long_max()
 393    {
 394       init.do_nothing();
 395       static cpp_dec_float val((std::numeric_limits<boost::ulong_long_type>::max)());
 396       return val;
 397    }
 398
 399    static const cpp_dec_float& eps()
 400    {
 401       init.do_nothing();
 402       static cpp_dec_float val(1.0, 1 - static_cast<int>(cpp_dec_float_digits10));
 403       return val;
 404    }
 405
 406    // Basic operations.
 407    cpp_dec_float& operator=(const cpp_dec_float& v) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<array_type&>() = std::declval<const array_type&>()))
 408    {
 409       data = v.data;
 410       exp = v.exp;
 411       neg = v.neg;
 412       fpclass = v.fpclass;
 413       prec_elem = v.prec_elem;
 414       return *this;
 415    }
 416
 417    template <unsigned D>
 418    cpp_dec_float& operator=(const cpp_dec_float<D>& f)
 419    {
 420       exp = f.exp;
 421       neg = f.neg;
 422       fpclass = static_cast<enum_fpclass_type>(static_cast<int>(f.fpclass));
 423       unsigned elems = (std::min)(f.prec_elem, cpp_dec_float_elem_number);
 424       std::copy(f.data.begin(), f.data.begin() + elems, data.begin());
 425       std::fill(data.begin() + elems, data.end(), 0);
 426       prec_elem = cpp_dec_float_elem_number;
 427       return *this;
 428    }
 429
 430    cpp_dec_float& operator=(boost::long_long_type v)
 431    {
 432       if(v < 0)
 433       {
 434          from_unsigned_long_long(-v);
 435          negate();
 436       }
 437       else
 438          from_unsigned_long_long(v);
 439       return *this;
 440    }
 441
 442    cpp_dec_float& operator=(boost::ulong_long_type v)
 443    {
 444       from_unsigned_long_long(v);
 445       return *this;
 446    }
 447
 448    cpp_dec_float& operator=(long double v);
 449
 450    cpp_dec_float& operator=(const char* v)
 451    {
 452       rd_string(v);
 453       return *this;
 454    }
 455
 456    cpp_dec_float& operator+=(const cpp_dec_float& v);
 457    cpp_dec_float& operator-=(const cpp_dec_float& v);
 458    cpp_dec_float& operator*=(const cpp_dec_float& v);
 459    cpp_dec_float& operator/=(const cpp_dec_float& v);
 460
 461    cpp_dec_float& add_unsigned_long_long(const boost::ulong_long_type n)
 462    {
 463       cpp_dec_float t;
 464       t.from_unsigned_long_long(n);
 465       return *this += t;
 466    }
 467
 468    cpp_dec_float& sub_unsigned_long_long(const boost::ulong_long_type n)
 469    {
 470       cpp_dec_float t;
 471       t.from_unsigned_long_long(n);
 472       return *this -= t;
 473    }
 474
 475    cpp_dec_float& mul_unsigned_long_long(const boost::ulong_long_type n);
 476    cpp_dec_float& div_unsigned_long_long(const boost::ulong_long_type n);
 477
 478    // Elementary primitives.
 479    cpp_dec_float& calculate_inv ();
 480    cpp_dec_float& calculate_sqrt();
 481
 482    void negate()
 483    {
 484       if(!iszero())
 485          neg = !neg;
 486    }
 487
 488    // Comparison functions
 489    bool isnan    BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_NaN); }
 490    bool isinf    BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_inf); }
 491    bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_finite); }
 492
 493    bool iszero () const
 494    {
 495       return ((fpclass == cpp_dec_float_finite) && (data[0u] == 0u));
 496    }
 497
 498    bool isone () const;
 499    bool isint () const;
 500    bool isneg () const { return neg; }
 501
 502    // Operators pre-increment and pre-decrement
 503    cpp_dec_float& operator++()
 504    {
 505       return *this += one();
 506    }
 507
 508    cpp_dec_float& operator--()
 509    {
 510       return *this -= one();
 511    }
 512
 513    std::string str(boost::intmax_t digits, std::ios_base::fmtflags f)const;
 514
 515    int compare(const cpp_dec_float& v)const;
 516
 517    template <class V>
 518    int compare(const V& v)const
 519    {
 520       cpp_dec_float<Digits10, ExponentType, Allocator> t;
 521       t = v;
 522       return compare(t);
 523    }
 524
 525    void swap(cpp_dec_float& v)
 526    {
 527       data.swap(v.data);
 528       std::swap(exp, v.exp);
 529       std::swap(neg, v.neg);
 530       std::swap(fpclass, v.fpclass);
 531       std::swap(prec_elem, v.prec_elem);
 532    }
 533
 534    double extract_double() const;
 535    long double extract_long_double() const;
 536    boost::long_long_type extract_signed_long_long() const;
 537    boost::ulong_long_type extract_unsigned_long_long() const;
 538    void extract_parts(double& mantissa, ExponentType& exponent) const;
 539    cpp_dec_float extract_integer_part() const;
 540
 541    void precision(const boost::int32_t prec_digits)
 542    {
 543       if(prec_digits >= cpp_dec_float_total_digits10)
 544       {
 545          prec_elem = cpp_dec_float_elem_number;
 546       }
 547       else
 548       {
 549          const boost::int32_t elems = static_cast<boost::int32_t>( static_cast<boost::int32_t>( (prec_digits + (cpp_dec_float_elem_digits10 / 2)) / cpp_dec_float_elem_digits10)
 550             + static_cast<boost::int32_t>(((prec_digits % cpp_dec_float_elem_digits10) != 0) ? 1 : 0));
 551
 552          prec_elem = (std::min)(cpp_dec_float_elem_number, (std::max)(elems, static_cast<boost::int32_t>(2)));
 553       }
 554    }
 555    static cpp_dec_float pow2(boost::long_long_type i);
 556    ExponentType order()const
 557    {
 558       const bool bo_order_is_zero = ((!(isfinite)()) || (data[0] == static_cast<boost::uint32_t>(0u)));
 559       //
 560       // Binary search to find the order of the leading term:
 561       //
 562       ExponentType prefix = 0;
 563
 564       if(data[0] >= 100000UL)
 565       {
 566          if(data[0] >= 10000000UL)
 567          {
 568             if(data[0] >= 100000000UL)
 569             {
 570                if(data[0] >= 1000000000UL)
 571                   prefix = 9;
 572                else
 573                   prefix = 8;
 574             }
 575             else
 576                prefix = 7;
 577          }
 578          else
 579          {
 580             if(data[0] >= 1000000UL)
 581                prefix = 6;
 582             else
 583                prefix = 5;
 584          }
 585       }
 586       else
 587       {
 588          if(data[0] >= 1000UL)
 589          {
 590             if(data[0] >= 10000UL)
 591                prefix = 4;
 592             else
 593                prefix = 3;
 594          }
 595          else
 596          {
 597             if(data[0] >= 100)
 598                prefix = 2;
 599             else if(data[0] >= 10)
 600                prefix = 1;
 601          }
 602       }
 603
 604       return (bo_order_is_zero ? static_cast<ExponentType>(0) : static_cast<ExponentType>(exp + prefix));
 605    }
 606
 607    template<class Archive>
 608    void serialize(Archive & ar, const unsigned int /*version*/)
 609    {
 610       for(unsigned i = 0; i < data.size(); ++i)
 611          ar & data[i];
 612       ar & exp;
 613       ar & neg;
 614       ar & fpclass;
 615       ar & prec_elem;
 616    }
 617
 618 private:
 619    static bool data_elem_is_non_zero_predicate(const boost::uint32_t& d) { return (d != static_cast<boost::uint32_t>(0u)); }
 620    static bool data_elem_is_non_nine_predicate(const boost::uint32_t& d) { return (d != static_cast<boost::uint32_t>(cpp_dec_float::cpp_dec_float_elem_mask - 1)); }
 621    static bool char_is_nonzero_predicate(const char& c) { return (c != static_cast<char>('0')); }
 622
 623    void from_unsigned_long_long(const boost::ulong_long_type u);
 624
 625    int cmp_data(const array_type& vd) const;
 626
 627
 628    static boost::uint32_t mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p);
 629    static boost::uint32_t mul_loop_n (boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p);
 630    static boost::uint32_t div_loop_n (boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p);
 631
 632    bool rd_string(const char* const s);
 633
 634    template <unsigned D, class ET, class A>
 635    friend class cpp_dec_float;
 636 };
 637
 638 template <unsigned Digits10, class ExponentType, class Allocator>
 639 typename cpp_dec_float<Digits10, ExponentType, Allocator>::initializer cpp_dec_float<Digits10, ExponentType, Allocator>::init;
 640
 641 template <unsigned Digits10, class ExponentType, class Allocator>
 642 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_radix;
 643 template <unsigned Digits10, class ExponentType, class Allocator>
 644 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_setting;
 645 template <unsigned Digits10, class ExponentType, class Allocator>
 646 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_limit_lo;
 647 template <unsigned Digits10, class ExponentType, class Allocator>
 648 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_limit_hi;
 649 template <unsigned Digits10, class ExponentType, class Allocator>
 650 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10;
 651 template <unsigned Digits10, class ExponentType, class Allocator>
 652 const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp;
 653 template <unsigned Digits10, class ExponentType, class Allocator>
 654 const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp;
 655 template <unsigned Digits10, class ExponentType, class Allocator>
 656 const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10;
 657 template <unsigned Digits10, class ExponentType, class Allocator>
 658 const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10;
 659 template <unsigned Digits10, class ExponentType, class Allocator>
 660 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_digits10;
 661 template <unsigned Digits10, class ExponentType, class Allocator>
 662 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_number_request;
 663 template <unsigned Digits10, class ExponentType, class Allocator>
 664 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_number;
 665 template <unsigned Digits10, class ExponentType, class Allocator>
 666 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_mask;
 667
 668 template <unsigned Digits10, class ExponentType, class Allocator>
 669 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator+=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v)
 670 {
 671    if((isnan)())
 672    {
 673       return *this;
 674    }
 675
 676    if((isinf)())
 677    {
 678       if((v.isinf)() && (isneg() != v.isneg()))
 679       {
 680          *this = nan();
 681       }
 682       return *this;
 683    }
 684
 685    if(iszero())
 686    {
 687       return operator=(v);
 688    }
 689
 690    if((v.isnan)() || (v.isinf)())
 691    {
 692       *this = v;
 693       return *this;
 694    }
 695
 696    // Get the offset for the add/sub operation.
 697    static const ExponentType max_delta_exp = static_cast<ExponentType>((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10);
 698
 699    const ExponentType ofs_exp = static_cast<ExponentType>(exp - v.exp);
 700
 701    // Check if the operation is out of range, requiring special handling.
 702    if(v.iszero() || (ofs_exp > max_delta_exp))
 703    {
 704       // Result is *this unchanged since v is negligible compared to *this.
 705       return *this;
 706    }
 707    else if(ofs_exp < -max_delta_exp)
 708    {
 709       // Result is *this = v since *this is negligible compared to v.
 710       return operator=(v);
 711    }
 712
 713    // Do the add/sub operation.
 714
 715    typename array_type::iterator p_u = data.begin();
 716    typename array_type::const_iterator p_v = v.data.begin();
 717    bool b_copy = false;
 718    const boost::int32_t ofs = static_cast<boost::int32_t>(static_cast<boost::int32_t>(ofs_exp) / cpp_dec_float_elem_digits10);
 719    array_type n_data;
 720
 721    if(neg == v.neg)
 722    {
 723       // Add v to *this, where the data array of either *this or v
 724       // might have to be treated with a positive, negative or zero offset.
 725       // The result is stored in *this. The data are added one element
 726       // at a time, each element with carry.
 727       if(ofs >= static_cast<boost::int32_t>(0))
 728       {
 729          std::copy(v.data.begin(), v.data.end() - static_cast<size_t>(ofs), n_data.begin() + static_cast<size_t>(ofs));
 730          std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(ofs), static_cast<boost::uint32_t>(0u));
 731          p_v = n_data.begin();
 732       }
 733       else
 734       {
 735          std::copy(data.begin(), data.end() - static_cast<size_t>(-ofs), n_data.begin() + static_cast<size_t>(-ofs));
 736          std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(-ofs), static_cast<boost::uint32_t>(0u));
 737          p_u = n_data.begin();
 738          b_copy = true;
 739       }
 740
 741       // Addition algorithm
 742       boost::uint32_t carry = static_cast<boost::uint32_t>(0u);
 743
 744       for(boost::int32_t j = static_cast<boost::int32_t>(cpp_dec_float_elem_number - static_cast<boost::int32_t>(1)); j >= static_cast<boost::int32_t>(0); j--)
 745       {
 746          boost::uint32_t t = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(p_u[j] + p_v[j]) + carry);
 747          carry = t / static_cast<boost::uint32_t>(cpp_dec_float_elem_mask);
 748          p_u[j] = static_cast<boost::uint32_t>(t - static_cast<boost::uint32_t>(carry * static_cast<boost::uint32_t>(cpp_dec_float_elem_mask)));
 749       }
 750
 751       if(b_copy)
 752       {
 753          data = n_data;
 754          exp = v.exp;
 755       }
 756
 757       // There needs to be a carry into the element -1 of the array data
 758       if(carry != static_cast<boost::uint32_t>(0u))
 759       {
 760          std::copy_backward(data.begin(), data.end() - static_cast<std::size_t>(1u), data.end());
 761          data[0] = carry;
 762          exp += static_cast<ExponentType>(cpp_dec_float_elem_digits10);
 763       }
 764    }
 765    else
 766    {
 767       // Subtract v from *this, where the data array of either *this or v
 768       // might have to be treated with a positive, negative or zero offset.
 769       if((ofs > static_cast<boost::int32_t>(0))
 770          || ( (ofs == static_cast<boost::int32_t>(0))
 771          && (cmp_data(v.data) > static_cast<boost::int32_t>(0)))
 772          )
 773       {
 774          // In this case, |u| > |v| and ofs is positive.
 775          // Copy the data of v, shifted down to a lower value
 776          // into the data array m_n. Set the operand pointer p_v
 777          // to point to the copied, shifted data m_n.
 778          std::copy(v.data.begin(), v.data.end() - static_cast<size_t>(ofs), n_data.begin() + static_cast<size_t>(ofs));
 779          std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(ofs), static_cast<boost::uint32_t>(0u));
 780          p_v = n_data.begin();
 781       }
 782       else
 783       {
 784          if(ofs != static_cast<boost::int32_t>(0))
 785          {
 786             // In this case, |u| < |v| and ofs is negative.
 787             // Shift the data of u down to a lower value.
 788             std::copy_backward(data.begin(), data.end() - static_cast<size_t>(-ofs), data.end());
 789             std::fill(data.begin(), data.begin() + static_cast<size_t>(-ofs), static_cast<boost::uint32_t>(0u));
 790          }
 791
 792          // Copy the data of v into the data array n_data.
 793          // Set the u-pointer p_u to point to m_n and the
 794          // operand pointer p_v to point to the shifted
 795          // data m_data.
 796          n_data = v.data;
 797          p_u = n_data.begin();
 798          p_v = data.begin();
 799          b_copy = true;
 800       }
 801
 802       boost::int32_t j;
 803
 804       // Subtraction algorithm
 805       boost::int32_t borrow = static_cast<boost::int32_t>(0);
 806
 807       for(j = static_cast<boost::int32_t>(cpp_dec_float_elem_number - static_cast<boost::int32_t>(1)); j >= static_cast<boost::int32_t>(0); j--)
 808       {
 809          boost::int32_t t = static_cast<boost::int32_t>(static_cast<boost::int32_t>( static_cast<boost::int32_t>(p_u[j])
 810             - static_cast<boost::int32_t>(p_v[j])) - borrow);
 811
 812          // Underflow? Borrow?
 813          if(t < static_cast<boost::int32_t>(0))
 814          {
 815             // Yes, underflow and borrow
 816             t += static_cast<boost::int32_t>(cpp_dec_float_elem_mask);
 817             borrow = static_cast<boost::int32_t>(1);
 818          }
 819          else
 820          {
 821             borrow = static_cast<boost::int32_t>(0);
 822          }
 823
 824          p_u[j] = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(t) % static_cast<boost::uint32_t>(cpp_dec_float_elem_mask));
 825       }
 826
 827       if(b_copy)
 828       {
 829          data = n_data;
 830          exp = v.exp;
 831          neg = v.neg;
 832       }
 833
 834       // Is it necessary to justify the data?
 835       const typename array_type::const_iterator first_nonzero_elem = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate);
 836
 837       if(first_nonzero_elem != data.begin())
 838       {
 839          if(first_nonzero_elem == data.end())
 840          {
 841             // This result of the subtraction is exactly zero.
 842             // Reset the sign and the exponent.
 843             neg = false;
 844             exp = static_cast<ExponentType>(0);
 845          }
 846          else
 847          {
 848             // Justify the data
 849             const std::size_t sj = static_cast<std::size_t>(std::distance<typename array_type::const_iterator>(data.begin(), first_nonzero_elem));
 850
 851             std::copy(data.begin() + static_cast<std::size_t>(sj), data.end(), data.begin());
 852             std::fill(data.end() - sj, data.end(), static_cast<boost::uint32_t>(0u));
 853
 854             exp -= static_cast<ExponentType>(sj * static_cast<std::size_t>(cpp_dec_float_elem_digits10));
 855          }
 856       }
 857    }
 858
 859    // Handle underflow.
 860    if(iszero())
 861       return (*this = zero());
 862
 863    // Check for potential overflow.
 864    const bool b_result_might_overflow  = (exp >= static_cast<ExponentType>(cpp_dec_float_max_exp10));
 865
 866    // Handle overflow.
 867    if(b_result_might_overflow)
 868    {
 869       const bool b_result_is_neg = neg;
 870       neg = false;
 871
 872       if(compare((cpp_dec_float::max)()) > 0)
 873         *this = inf();
 874
 875       neg = b_result_is_neg;
 876    }
 877
 878    return *this;
 879 }
 880
 881 template <unsigned Digits10, class ExponentType, class Allocator>
 882 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator-=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v)
 883 {
 884    // Use *this - v = -(-*this + v).
 885    negate();
 886    *this += v;
 887    negate();
 888    return *this;
 889 }
 890
 891 template <unsigned Digits10, class ExponentType, class Allocator>
 892 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator*=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v)
 893 {
 894    // Evaluate the sign of the result.
 895    const bool b_result_is_neg = (neg != v.neg);
 896
 897    // Artificially set the sign of the result to be positive.
 898    neg = false;
 899
 900    // Handle special cases like zero, inf and NaN.
 901    const bool b_u_is_inf  = (isinf)();
 902    const bool b_v_is_inf  = (v.isinf)();
 903    const bool b_u_is_zero = iszero();
 904    const bool b_v_is_zero = v.iszero();
 905
 906    if(   ((isnan)() || (v.isnan)())
 907       || (b_u_is_inf && b_v_is_zero)
 908       || (b_v_is_inf && b_u_is_zero)
 909       )
 910    {
 911       *this = nan();
 912       return *this;
 913    }
 914
 915    if(b_u_is_inf || b_v_is_inf)
 916    {
 917       *this = inf();
 918       if(b_result_is_neg)
 919          negate();
 920       return *this;
 921    }
 922
 923    if(b_u_is_zero || b_v_is_zero)
 924    {
 925       return *this = zero();
 926    }
 927
 928    // Check for potential overflow or underflow.
 929    const bool b_result_might_overflow  = ((exp + v.exp) >= static_cast<ExponentType>(cpp_dec_float_max_exp10));
 930    const bool b_result_might_underflow = ((exp + v.exp) <= static_cast<ExponentType>(cpp_dec_float_min_exp10));
 931
 932    // Set the exponent of the result.
 933    exp += v.exp;
 934
 935    const boost::int32_t prec_mul = (std::min)(prec_elem, v.prec_elem);
 936
 937    const boost::uint32_t carry = mul_loop_uv(data.data(), v.data.data(), prec_mul);
 938
 939    // Handle a potential carry.
 940    if(carry != static_cast<boost::uint32_t>(0u))
 941    {
 942       exp += cpp_dec_float_elem_digits10;
 943
 944       // Shift the result of the multiplication one element to the right...
 945       std::copy_backward(data.begin(),
 946                          data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)),
 947                          data.begin() + static_cast<std::size_t>(prec_elem));
 948
 949       // ... And insert the carry.
 950       data.front() = carry;
 951    }
 952
 953    // Handle overflow.
 954    if(b_result_might_overflow && (compare((cpp_dec_float::max)()) > 0))
 955    {
 956       *this = inf();
 957    }
 958
 959    // Handle underflow.
 960    if(b_result_might_underflow && (compare((cpp_dec_float::min)()) < 0))
 961    {
 962       *this = zero();
 963
 964       return *this;
 965    }
 966
 967    // Set the sign of the result.
 968    neg = b_result_is_neg;
 969
 970    return *this;
 971 }
 972
 973 template <unsigned Digits10, class ExponentType, class Allocator>
 974 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator/=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v)
 975 {
 976    if(iszero())
 977    {
 978       if((v.isnan)())
 979       {
 980          return *this = v;
 981       }
 982       else if(v.iszero())
 983       {
 984          return *this = nan();
 985       }
 986    }
 987
 988    const bool u_and_v_are_finite_and_identical = ( (isfinite)()
 989       && (fpclass == v.fpclass)
 990       && (exp == v.exp)
 991       && (cmp_data(v.data) == static_cast<boost::int32_t>(0)));
 992
 993    if(u_and_v_are_finite_and_identical)
 994    {
 995       if(neg != v.neg)
 996       {
 997          *this = one();
 998          negate();
 999       }
1000       else
1001          *this = one();
1002       return *this;
1003    }
1004    else
1005    {
1006       cpp_dec_float t(v);
1007       t.calculate_inv();
1008       return operator*=(t);
1009    }
1010 }
1011
1012 template <unsigned Digits10, class ExponentType, class Allocator>
1013 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::mul_unsigned_long_long(const boost::ulong_long_type n)
1014 {
1015    // Multiply *this with a constant boost::ulong_long_type.
1016
1017    // Evaluate the sign of the result.
1018    const bool b_neg = neg;
1019
1020    // Artificially set the sign of the result to be positive.
1021    neg = false;
1022
1023    // Handle special cases like zero, inf and NaN.
1024    const bool b_u_is_inf = (isinf)();
1025    const bool b_n_is_zero = (n == static_cast<boost::int32_t>(0));
1026
1027    if((isnan)() || (b_u_is_inf && b_n_is_zero))
1028    {
1029       return (*this = nan());
1030    }
1031
1032    if(b_u_is_inf)
1033    {
1034       *this = inf();
1035       if(b_neg)
1036          negate();
1037       return *this;
1038    }
1039
1040    if(iszero() || b_n_is_zero)
1041    {
1042       // Multiplication by zero.
1043       return *this = zero();
1044    }
1045
1046    if(n >= static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask))
1047    {
1048       neg = b_neg;
1049       cpp_dec_float t;
1050       t = n;
1051       return operator*=(t);
1052    }
1053
1054    if(n == static_cast<boost::ulong_long_type>(1u))
1055    {
1056       neg = b_neg;
1057       return *this;
1058    }
1059
1060    // Set up the multiplication loop.
1061    const boost::uint32_t nn = static_cast<boost::uint32_t>(n);
1062    const boost::uint32_t carry = mul_loop_n(data.data(), nn, prec_elem);
1063
1064    // Handle the carry and adjust the exponent.
1065    if(carry != static_cast<boost::uint32_t>(0u))
1066    {
1067       exp += static_cast<ExponentType>(cpp_dec_float_elem_digits10);
1068
1069       // Shift the result of the multiplication one element to the right.
1070       std::copy_backward(data.begin(),
1071          data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)),
1072          data.begin() + static_cast<std::size_t>(prec_elem));
1073
1074       data.front() = static_cast<boost::uint32_t>(carry);
1075    }
1076
1077    // Check for potential overflow.
1078    const bool b_result_might_overflow = (exp >= cpp_dec_float_max_exp10);
1079
1080    // Handle overflow.
1081    if(b_result_might_overflow && (compare((cpp_dec_float::max)()) > 0))
1082    {
1083       *this = inf();
1084    }
1085
1086    // Set the sign.
1087    neg = b_neg;
1088
1089    return *this;
1090 }
1091
1092 template <unsigned Digits10, class ExponentType, class Allocator>
1093 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::div_unsigned_long_long(const boost::ulong_long_type n)
1094 {
1095    // Divide *this by a constant boost::ulong_long_type.
1096
1097    // Evaluate the sign of the result.
1098    const bool b_neg = neg;
1099
1100    // Artificially set the sign of the result to be positive.
1101    neg = false;
1102
1103    // Handle special cases like zero, inf and NaN.
1104    if((isnan)())
1105    {
1106       return *this;
1107    }
1108
1109    if((isinf)())
1110    {
1111       *this = inf();
1112       if(b_neg)
1113          negate();
1114       return *this;
1115    }
1116
1117    if(n == static_cast<boost::ulong_long_type>(0u))
1118    {
1119       // Divide by 0.
1120       if(iszero())
1121       {
1122          *this = nan();
1123          return *this;
1124       }
1125       else
1126       {
1127          *this = inf();
1128          if(isneg())
1129             negate();
1130          return *this;
1131       }
1132    }
1133
1134    if(iszero())
1135    {
1136       return *this;
1137    }
1138
1139    if(n >= static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask))
1140    {
1141       neg = b_neg;
1142       cpp_dec_float t;
1143       t = n;
1144       return operator/=(t);
1145    }
1146
1147    const boost::uint32_t nn = static_cast<boost::uint32_t>(n);
1148
1149    if(nn > static_cast<boost::uint32_t>(1u))
1150    {
1151       // Do the division loop.
1152       const boost::uint32_t prev = div_loop_n(data.data(), nn, prec_elem);
1153
1154       // Determine if one leading zero is in the result data.
1155       if(data[0] == static_cast<boost::uint32_t>(0u))
1156       {
1157          // Adjust the exponent
1158          exp -= static_cast<ExponentType>(cpp_dec_float_elem_digits10);
1159
1160          // Shift result of the division one element to the left.
1161          std::copy(data.begin() + static_cast<std::size_t>(1u),
1162             data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)),
1163             data.begin());
1164
1165          data[prec_elem - static_cast<boost::int32_t>(1)] = static_cast<boost::uint32_t>(static_cast<boost::uint64_t>(prev * static_cast<boost::uint64_t>(cpp_dec_float_elem_mask)) / nn);
1166       }
1167    }
1168
1169    // Check for potential underflow.
1170    const bool b_result_might_underflow = (exp <= cpp_dec_float_min_exp10);
1171
1172    // Handle underflow.
1173    if(b_result_might_underflow && (compare((cpp_dec_float::min)()) < 0))
1174       return (*this = zero());
1175
1176    // Set the sign of the result.
1177    neg = b_neg;
1178
1179    return *this;
1180 }
1181
1182 template <unsigned Digits10, class ExponentType, class Allocator>
1183 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::calculate_inv()
1184 {
1185    // Compute the inverse of *this.
1186    const bool b_neg = neg;
1187
1188    neg = false;
1189
1190    // Handle special cases like zero, inf and NaN.
1191    if(iszero())
1192    {
1193       *this = inf();
1194       if(b_neg)
1195          negate();
1196       return *this;
1197    }
1198
1199    if((isnan)())
1200    {
1201       return *this;
1202    }
1203
1204    if((isinf)())
1205    {
1206       return *this = zero();
1207    }
1208
1209    if(isone())
1210    {
1211       if(b_neg)
1212          negate();
1213       return *this;
1214    }
1215
1216    // Save the original *this.
1217    cpp_dec_float<Digits10, ExponentType, Allocator> x(*this);
1218
1219    // Generate the initial estimate using division.
1220    // Extract the mantissa and exponent for a "manual"
1221    // computation of the estimate.
1222    double dd;
1223    ExponentType ne;
1224    x.extract_parts(dd, ne);
1225
1226    // Do the inverse estimate using double precision estimates of mantissa and exponent.
1227    operator=(cpp_dec_float<Digits10, ExponentType, Allocator>(1.0 / dd, -ne));
1228
1229    // Compute the inverse of *this. Quadratically convergent Newton-Raphson iteration
1230    // is used. During the iterative steps, the precision of the calculation is limited
1231    // to the minimum required in order to minimize the run-time.
1232
1233    static const boost::int32_t double_digits10_minus_a_few = std::numeric_limits<double>::digits10 - 3;
1234
1235    for(boost::int32_t digits = double_digits10_minus_a_few; digits <= cpp_dec_float_total_digits10; digits *= static_cast<boost::int32_t>(2))
1236    {
1237       // Adjust precision of the terms.
1238       precision(static_cast<boost::int32_t>((digits + 10) * static_cast<boost::int32_t>(2)));
1239       x.precision(static_cast<boost::int32_t>((digits + 10) * static_cast<boost::int32_t>(2)));
1240
1241       // Next iteration.
1242       cpp_dec_float t(*this);
1243       t *= x;
1244       t -= two();
1245       t.negate();
1246       *this *= t;
1247    }
1248
1249    neg = b_neg;
1250
1251    prec_elem = cpp_dec_float_elem_number;
1252
1253    return *this;
1254 }
1255
1256 template <unsigned Digits10, class ExponentType, class Allocator>
1257 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::calculate_sqrt()
1258 {
1259    // Compute the square root of *this.
1260
1261    if((isinf)() && !isneg())
1262    {
1263       return *this;
1264    }
1265
1266    if(isneg() || (!(isfinite)()))
1267    {
1268       *this = nan();
1269       errno = EDOM;
1270       return *this;
1271    }
1272
1273    if(iszero() || isone())
1274    {
1275       return *this;
1276    }
1277
1278    // Save the original *this.
1279    cpp_dec_float<Digits10, ExponentType, Allocator> x(*this);
1280
1281    // Generate the initial estimate using division.
1282    // Extract the mantissa and exponent for a "manual"
1283    // computation of the estimate.
1284    double dd;
1285    ExponentType ne;
1286    extract_parts(dd, ne);
1287
1288    // Force the exponent to be an even multiple of two.
1289    if((ne % static_cast<ExponentType>(2)) != static_cast<ExponentType>(0))
1290    {
1291       ++ne;
1292       dd /= 10.0;
1293    }
1294
1295    // Setup the iteration.
1296    // Estimate the square root using simple manipulations.
1297    const double sqd = std::sqrt(dd);
1298
1299    *this = cpp_dec_float<Digits10, ExponentType, Allocator>(sqd, static_cast<ExponentType>(ne / static_cast<ExponentType>(2)));
1300
1301    // Estimate 1.0 / (2.0 * x0) using simple manipulations.
1302    cpp_dec_float<Digits10, ExponentType, Allocator> vi(0.5 / sqd, static_cast<ExponentType>(-ne / static_cast<ExponentType>(2)));
1303
1304    // Compute the square root of x. Coupled Newton iteration
1305    // as described in "Pi Unleashed" is used. During the
1306    // iterative steps, the precision of the calculation is
1307    // limited to the minimum required in order to minimize
1308    // the run-time.
1309    //
1310    // Book references:
1311    // http://www.jjj.de/pibook/pibook.html
1312    // http://www.amazon.com/exec/obidos/tg/detail/-/3540665722/qid=1035535482/sr=8-7/ref=sr_8_7/104-3357872-6059916?v=glance&n=507846
1313
1314    static const boost::uint32_t double_digits10_minus_a_few = std::numeric_limits<double>::digits10 - 3;
1315
1316    for(boost::int32_t digits = double_digits10_minus_a_few; digits <= cpp_dec_float_total_digits10; digits *= 2u)
1317    {
1318       // Adjust precision of the terms.
1319       precision((digits + 10) * 2);
1320       vi.precision((digits + 10) * 2);
1321
1322       // Next iteration of vi
1323       cpp_dec_float t(*this);
1324       t *= vi;
1325       t.negate();
1326       t.mul_unsigned_long_long(2u);
1327       t += one();
1328       t *= vi;
1329       vi += t;
1330
1331       // Next iteration of *this
1332       t = *this;
1333       t *= *this;
1334       t.negate();
1335       t += x;
1336       t *= vi;
1337       *this += t;
1338    }
1339
1340    prec_elem = cpp_dec_float_elem_number;
1341
1342    return *this;
1343 }
1344
1345 template <unsigned Digits10, class ExponentType, class Allocator>
1346 int cpp_dec_float<Digits10, ExponentType, Allocator>::cmp_data(const array_type& vd) const
1347 {
1348    // Compare the data of *this with those of v.
1349    // Return +1 for *this > v
1350    // 0 for *this = v
1351    // -1 for *this < v
1352
1353    const std::pair<typename array_type::const_iterator, typename array_type::const_iterator> mismatch_pair = std::mismatch(data.begin(), data.end(), vd.begin());
1354
1355    const bool is_equal = ((mismatch_pair.first == data.end()) && (mismatch_pair.second == vd.end()));
1356
1357    if(is_equal)
1358    {
1359       return 0;
1360    }
1361    else
1362    {
1363       return ((*mismatch_pair.first > *mismatch_pair.second) ? 1 : -1);
1364    }
1365 }
1366
1367 template <unsigned Digits10, class ExponentType, class Allocator>
1368 int cpp_dec_float<Digits10, ExponentType, Allocator>::compare(const cpp_dec_float& v) const
1369 {
1370    // Compare v with *this.
1371    // Return +1 for *this > v
1372    // 0 for *this = v
1373    // -1 for *this < v
1374
1375    // Handle all non-finite cases.
1376    if((!(isfinite)()) || (!(v.isfinite)()))
1377    {
1378       // NaN can never equal NaN. Return an implementation-dependent
1379       // signed result. Also note that comparison of NaN with NaN
1380       // using operators greater-than or less-than is undefined.
1381       if((isnan)() || (v.isnan)()) { return ((isnan)() ? 1 : -1); }
1382
1383       if((isinf)() && (v.isinf)())
1384       {
1385          // Both *this and v are infinite. They are equal if they have the same sign.
1386          // Otherwise, *this is less than v if and only if *this is negative.
1387          return ((neg == v.neg) ? 0 : (neg ? -1 : 1));
1388       }
1389
1390       if((isinf)())
1391       {
1392          // *this is infinite, but v is finite.
1393          // So negative infinite *this is less than any finite v.
1394          // Whereas positive infinite *this is greater than any finite v.
1395          return (isneg() ? -1 : 1);
1396       }
1397       else
1398       {
1399          // *this is finite, and v is infinite.
1400          // So any finite *this is greater than negative infinite v.
1401          // Whereas any finite *this is less than positive infinite v.
1402          return (v.neg ? 1 : -1);
1403       }
1404    }
1405
1406    // And now handle all *finite* cases.
1407    if(iszero())
1408    {
1409       // The value of *this is zero and v is either zero or non-zero.
1410       return (v.iszero() ? 0
1411          : (v.neg ? 1 : -1));
1412    }
1413    else if(v.iszero())
1414    {
1415       // The value of v is zero and *this is non-zero.
1416       return (neg ? -1 : 1);
1417    }
1418    else
1419    {
1420       // Both *this and v are non-zero.
1421
1422       if(neg != v.neg)
1423       {
1424          // The signs are different.
1425          return (neg ? -1 : 1);
1426       }
1427       else if(exp != v.exp)
1428       {
1429          // The signs are the same and the exponents are different.
1430          const int val_cexpression = ((exp < v.exp) ? 1 : -1);
1431
1432          return (neg ? val_cexpression : -val_cexpression);
1433       }
1434       else
1435       {
1436          // The signs are the same and the exponents are the same.
1437          // Compare the data.
1438          const int val_cmp_data = cmp_data(v.data);
1439
1440          return ((!neg) ? val_cmp_data : -val_cmp_data);
1441       }
1442    }
1443 }
1444
1445 template <unsigned Digits10, class ExponentType, class Allocator>
1446 bool cpp_dec_float<Digits10, ExponentType, Allocator>::isone() const
1447 {
1448    // Check if the value of *this is identically 1 or very close to 1.
1449
1450    const bool not_negative_and_is_finite = ((!neg) && (isfinite)());
1451
1452    if(not_negative_and_is_finite)
1453    {
1454       if((data[0u] == static_cast<boost::uint32_t>(1u)) && (exp == static_cast<ExponentType>(0)))
1455       {
1456          const typename array_type::const_iterator it_non_zero = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate);
1457          return (it_non_zero == data.end());
1458       }
1459       else if((data[0u] == static_cast<boost::uint32_t>(cpp_dec_float_elem_mask - 1)) && (exp == static_cast<ExponentType>(-cpp_dec_float_elem_digits10)))
1460       {
1461          const typename array_type::const_iterator it_non_nine = std::find_if(data.begin(), data.end(), data_elem_is_non_nine_predicate);
1462          return (it_non_nine == data.end());
1463       }
1464    }
1465
1466    return false;
1467 }
1468
1469 template <unsigned Digits10, class ExponentType, class Allocator>
1470 bool cpp_dec_float<Digits10, ExponentType, Allocator>::isint() const
1471 {
1472    if(fpclass != cpp_dec_float_finite) { return false; }
1473
1474    if(iszero()) { return true; }
1475
1476    if(exp < static_cast<ExponentType>(0)) { return false; } // |*this| < 1.
1477
1478    const typename array_type::size_type offset_decimal_part = static_cast<typename array_type::size_type>(exp / cpp_dec_float_elem_digits10) + 1u;
1479
1480    if(offset_decimal_part >= static_cast<typename array_type::size_type>(cpp_dec_float_elem_number))
1481    {
1482       // The number is too large to resolve the integer part.
1483       // It considered to be a pure integer.
1484       return true;
1485    }
1486
1487    typename array_type::const_iterator it_non_zero = std::find_if(data.begin() + offset_decimal_part, data.end(), data_elem_is_non_zero_predicate);
1488
1489    return (it_non_zero == data.end());
1490 }
1491
1492 template <unsigned Digits10, class ExponentType, class Allocator>
1493 void cpp_dec_float<Digits10, ExponentType, Allocator>::extract_parts(double& mantissa, ExponentType& exponent) const
1494 {
1495    // Extract the approximate parts mantissa and base-10 exponent from the input cpp_dec_float<Digits10, ExponentType, Allocator> value x.
1496
1497    // Extracts the mantissa and exponent.
1498    exponent = exp;
1499
1500    boost::uint32_t p10 = static_cast<boost::uint32_t>(1u);
1501    boost::uint32_t test = data[0u];
1502
1503    for(;;)
1504    {
1505       test /= static_cast<boost::uint32_t>(10u);
1506
1507       if(test == static_cast<boost::uint32_t>(0u))
1508       {
1509          break;
1510       }
1511
1512       p10 *= static_cast<boost::uint32_t>(10u);
1513       ++exponent;
1514    }
1515
1516    // Establish the upper bound of limbs for extracting the double.
1517    const int max_elem_in_double_count = static_cast<int>(static_cast<boost::int32_t>(std::numeric_limits<double>::digits10) / cpp_dec_float_elem_digits10)
1518                                          + (static_cast<int>(static_cast<boost::int32_t>(std::numeric_limits<double>::digits10) % cpp_dec_float_elem_digits10) != 0 ? 1 : 0)
1519                                          + 1;
1520
1521    // And make sure this upper bound stays within bounds of the elems.
1522    const std::size_t max_elem_extract_count = static_cast<std::size_t>((std::min)(static_cast<boost::int32_t>(max_elem_in_double_count), cpp_dec_float_elem_number));
1523
1524    // Extract into the mantissa the first limb, extracted as a double.
1525    mantissa = static_cast<double>(data[0]);
1526    double scale = 1.0;
1527
1528    // Extract the rest of the mantissa piecewise from the limbs.
1529    for(std::size_t i = 1u; i < max_elem_extract_count; i++)
1530    {
1531      scale /= static_cast<double>(cpp_dec_float_elem_mask);
1532      mantissa += (static_cast<double>(data[i]) * scale);
1533    }
1534
1535    mantissa /= static_cast<double>(p10);
1536
1537    if(neg) { mantissa = -mantissa; }
1538 }
1539
1540 template <unsigned Digits10, class ExponentType, class Allocator>
1541 double cpp_dec_float<Digits10, ExponentType, Allocator>::extract_double() const
1542 {
1543    // Returns the double conversion of a cpp_dec_float<Digits10, ExponentType, Allocator>.
1544
1545    // Check for non-normal cpp_dec_float<Digits10, ExponentType, Allocator>.
1546    if(!(isfinite)())
1547    {
1548       if((isnan)())
1549       {
1550          return std::numeric_limits<double>::quiet_NaN();
1551       }
1552       else
1553       {
1554          return ((!neg) ? std::numeric_limits<double>::infinity()
1555             : -std::numeric_limits<double>::infinity());
1556       }
1557    }
1558
1559    cpp_dec_float<Digits10, ExponentType, Allocator> xx(*this);
1560    if(xx.isneg())
1561       xx.negate();
1562
1563    // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is zero.
1564    if(iszero() || (xx.compare(double_min()) < 0))
1565    {
1566       return 0.0;
1567    }
1568
1569    // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> exceeds the maximum of double.
1570    if(xx.compare(double_max()) > 0)
1571    {
1572       return ((!neg) ? std::numeric_limits<double>::infinity()
1573          : -std::numeric_limits<double>::infinity());
1574    }
1575
1576    std::stringstream ss;
1577
1578    ss << str(std::numeric_limits<double>::digits10 + (2 + 1), std::ios_base::scientific);
1579
1580    double d;
1581    ss >> d;
1582
1583    return d;
1584 }
1585
1586 template <unsigned Digits10, class ExponentType, class Allocator>
1587 long double cpp_dec_float<Digits10, ExponentType, Allocator>::extract_long_double() const
1588 {
1589    // Returns the long double conversion of a cpp_dec_float<Digits10, ExponentType, Allocator>.
1590
1591    // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is subnormal.
1592    if(!(isfinite)())
1593    {
1594       if((isnan)())
1595       {
1596          return std::numeric_limits<long double>::quiet_NaN();
1597       }
1598       else
1599       {
1600          return ((!neg) ? std::numeric_limits<long double>::infinity()
1601             : -std::numeric_limits<long double>::infinity());
1602       }
1603    }
1604
1605    cpp_dec_float<Digits10, ExponentType, Allocator> xx(*this);
1606    if(xx.isneg())
1607       xx.negate();
1608
1609    // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is zero.
1610    if(iszero() || (xx.compare(long_double_min()) < 0))
1611    {
1612       return static_cast<long double>(0.0);
1613    }
1614
1615    // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> exceeds the maximum of double.
1616    if(xx.compare(long_double_max()) > 0)
1617    {
1618       return ((!neg) ? std::numeric_limits<long double>::infinity()
1619          : -std::numeric_limits<long double>::infinity());
1620    }
1621
1622    std::stringstream ss;
1623
1624    ss << str(std::numeric_limits<long double>::digits10 + (2 + 1), std::ios_base::scientific);
1625
1626    long double ld;
1627    ss >> ld;
1628
1629    return ld;
1630 }
1631
1632 template <unsigned Digits10, class ExponentType, class Allocator>
1633 boost::long_long_type cpp_dec_float<Digits10, ExponentType, Allocator>::extract_signed_long_long() const
1634 {
1635    // Extracts a signed long long from *this.
1636    // If (x > maximum of long long) or (x < minimum of long long),
1637    // then the maximum or minimum of long long is returned accordingly.
1638
1639    if(exp < static_cast<ExponentType>(0))
1640    {
1641       return static_cast<boost::long_long_type>(0);
1642    }
1643
1644    const bool b_neg = isneg();
1645
1646    boost::ulong_long_type val;
1647
1648    if((!b_neg) && (compare(long_long_max()) > 0))
1649    {
1650       return (std::numeric_limits<boost::long_long_type>::max)();
1651    }
1652    else if(b_neg && (compare(long_long_min()) < 0))
1653    {
1654       return (std::numeric_limits<boost::long_long_type>::min)();
1655    }
1656    else
1657    {
1658       // Extract the data into an boost::ulong_long_type value.
1659       cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part());
1660       if(xn.isneg())
1661          xn.negate();
1662
1663       val = static_cast<boost::ulong_long_type>(xn.data[0]);
1664
1665       const boost::int32_t imax = (std::min)(static_cast<boost::int32_t>(static_cast<boost::int32_t>(xn.exp) / cpp_dec_float_elem_digits10), static_cast<boost::int32_t>(cpp_dec_float_elem_number - static_cast<boost::int32_t>(1)));
1666
1667       for(boost::int32_t i = static_cast<boost::int32_t>(1); i <= imax; i++)
1668       {
1669          val *= static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask);
1670          val += static_cast<boost::ulong_long_type>(xn.data[i]);
1671       }
1672    }
1673
1674    if (!b_neg)
1675    {
1676       return static_cast<boost::long_long_type>(val);
1677    }
1678    else
1679    {
1680       // This strange expression avoids a hardware trap in the corner case
1681       // that val is the most negative value permitted in boost::long_long_type.
1682       // See https://svn.boost.org/trac/boost/ticket/9740.
1683       //
1684       boost::long_long_type sval = static_cast<boost::long_long_type>(val - 1);
1685       sval = -sval;
1686       --sval;
1687       return sval;
1688    }
1689 }
1690
1691 template <unsigned Digits10, class ExponentType, class Allocator>
1692 boost::ulong_long_type cpp_dec_float<Digits10, ExponentType, Allocator>::extract_unsigned_long_long() const
1693 {
1694    // Extracts an boost::ulong_long_type from *this.
1695    // If x exceeds the maximum of boost::ulong_long_type,
1696    // then the maximum of boost::ulong_long_type is returned.
1697    // If x is negative, then the boost::ulong_long_type cast of
1698    // the long long extracted value is returned.
1699
1700    if(isneg())
1701    {
1702       return static_cast<boost::ulong_long_type>(extract_signed_long_long());
1703    }
1704
1705    if(exp < static_cast<ExponentType>(0))
1706    {
1707       return static_cast<boost::ulong_long_type>(0u);
1708    }
1709
1710    const cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part());
1711
1712    boost::ulong_long_type val;
1713
1714    if(xn.compare(ulong_long_max()) > 0)
1715    {
1716       return (std::numeric_limits<boost::ulong_long_type>::max)();
1717    }
1718    else
1719    {
1720       // Extract the data into an boost::ulong_long_type value.
1721       val = static_cast<boost::ulong_long_type>(xn.data[0]);
1722
1723       const boost::int32_t imax = (std::min)(static_cast<boost::int32_t>(static_cast<boost::int32_t>(xn.exp) / cpp_dec_float_elem_digits10), static_cast<boost::int32_t>(cpp_dec_float_elem_number - static_cast<boost::int32_t>(1)));
1724
1725       for(boost::int32_t i = static_cast<boost::int32_t>(1); i <= imax; i++)
1726       {
1727          val *= static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask);
1728          val += static_cast<boost::ulong_long_type>(xn.data[i]);
1729       }
1730    }
1731
1732    return val;
1733 }
1734
1735 template <unsigned Digits10, class ExponentType, class Allocator>
1736 cpp_dec_float<Digits10, ExponentType, Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>::extract_integer_part() const
1737 {
1738    // Compute the signed integer part of x.
1739
1740    if(!(isfinite)())
1741    {
1742       return *this;
1743    }
1744
1745    if(exp < static_cast<ExponentType>(0))
1746    {
1747       // The absolute value of the number is smaller than 1.
1748       // Thus the integer part is zero.
1749       return zero();
1750    }
1751
1752    // Truncate the digits from the decimal part, including guard digits
1753    // that do not belong to the integer part.
1754
1755    // Make a local copy.
1756    cpp_dec_float<Digits10, ExponentType, Allocator> x = *this;
1757
1758    // Clear out the decimal portion
1759    const size_t first_clear = (static_cast<size_t>(x.exp) / static_cast<size_t>(cpp_dec_float_elem_digits10)) + 1u;
1760    const size_t last_clear = static_cast<size_t>(cpp_dec_float_elem_number);
1761
1762    if(first_clear < last_clear)
1763       std::fill(x.data.begin() + first_clear, x.data.begin() + last_clear, static_cast<boost::uint32_t>(0u));
1764
1765    return x;
1766 }
1767
1768 template <unsigned Digits10, class ExponentType, class Allocator>
1769 std::string cpp_dec_float<Digits10, ExponentType, Allocator>::str(boost::intmax_t number_of_digits, std::ios_base::fmtflags f) const
1770 {
1771    if((this->isinf)())
1772    {
1773       if(this->isneg())
1774          return "-inf";
1775       else if(f & std::ios_base::showpos)
1776          return "+inf";
1777       else
1778          return "inf";
1779    }
1780    else if((this->isnan)())
1781    {
1782       return "nan";
1783    }
1784
1785    std::string str;
1786    boost::intmax_t org_digits(number_of_digits);
1787    ExponentType my_exp = order();
1788
1789    if(number_of_digits == 0)
1790       number_of_digits = cpp_dec_float_total_digits10;
1791
1792    if(f & std::ios_base::fixed)
1793    {
1794       number_of_digits += my_exp + 1;
1795    }
1796    else if(f & std::ios_base::scientific)
1797       ++number_of_digits;
1798    // Determine the number of elements needed to provide the requested digits from cpp_dec_float<Digits10, ExponentType, Allocator>.
1799    const std::size_t number_of_elements = (std::min)(static_cast<std::size_t>((number_of_digits / static_cast<std::size_t>(cpp_dec_float_elem_digits10)) + 2u),
1800       static_cast<std::size_t>(cpp_dec_float_elem_number));
1801
1802    // Extract the remaining digits from cpp_dec_float<Digits10, ExponentType, Allocator> after the decimal point.
1803    str = boost::lexical_cast<std::string>(data[0]);
1804
1805    // Extract all of the digits from cpp_dec_float<Digits10, ExponentType, Allocator>, beginning with the first data element.
1806    for(std::size_t i = static_cast<std::size_t>(1u); i < number_of_elements; i++)
1807    {
1808       std::stringstream ss;
1809
1810       ss << std::setw(static_cast<std::streamsize>(cpp_dec_float_elem_digits10))
1811          << std::setfill(static_cast<char>('0'))
1812          << data[i];
1813
1814       str += ss.str();
1815    }
1816
1817    bool have_leading_zeros = false;
1818
1819    if(number_of_digits == 0)
1820    {
1821       // We only get here if the output format is "fixed" and we just need to
1822       // round the first non-zero digit.
1823       number_of_digits -= my_exp + 1; // reset to original value
1824       str.insert(static_cast<std::string::size_type>(0), std::string::size_type(number_of_digits), '0');
1825       have_leading_zeros = true;
1826    }
1827
1828    if(number_of_digits < 0)
1829    {
1830       str = "0";
1831       if(isneg())
1832          str.insert(static_cast<std::string::size_type>(0), 1, '-');
1833       boost::multiprecision::detail::format_float_string(str, 0, number_of_digits - my_exp - 1, f, this->iszero());
1834       return str;
1835    }
1836    else
1837    {
1838       // Cut the output to the size of the precision.
1839       if(str.length() > static_cast<std::string::size_type>(number_of_digits))
1840       {
1841          // Get the digit after the last needed digit for rounding
1842          const boost::uint32_t round = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(str[static_cast<std::string::size_type>(number_of_digits)]) - static_cast<boost::uint32_t>('0'));
1843
1844          bool need_round_up = round >= 5u;
1845
1846          if(round == 5u)
1847          {
1848             const boost::uint32_t ix = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(str[static_cast<std::string::size_type>(number_of_digits - 1)]) - static_cast<boost::uint32_t>('0'));
1849             if((ix & 1u) == 0)
1850             {
1851                // We have an even digit followed by a 5, so we might not actually need to round up
1852                // if all the remaining digits are zero:
1853                if(str.find_first_not_of('0', static_cast<std::string::size_type>(number_of_digits + 1)) == std::string::npos)
1854                {
1855                   bool all_zeros = true;
1856                   // No none-zero trailing digits in the string, now check whatever parts we didn't convert to the string:
1857                   for(std::size_t i = number_of_elements; i < data.size(); i++)
1858                   {
1859                      if(data[i])
1860                      {
1861                         all_zeros = false;
1862                         break;
1863                      }
1864                   }
1865                   if(all_zeros)
1866                      need_round_up = false; // tie break - round to even.
1867                }
1868             }
1869          }
1870
1871          // Truncate the string
1872          str.erase(static_cast<std::string::size_type>(number_of_digits));
1873
1874          if(need_round_up)
1875          {
1876             std::size_t ix = static_cast<std::size_t>(str.length() - 1u);
1877
1878             // Every trailing 9 must be rounded up
1879             while(ix && (static_cast<boost::int32_t>(str.at(ix)) - static_cast<boost::int32_t>('0') == static_cast<boost::int32_t>(9)))
1880             {
1881                str.at(ix) = static_cast<char>('0');
1882                --ix;
1883             }
1884
1885             if(!ix)
1886             {
1887                // There were nothing but trailing nines.
1888                if(static_cast<boost::int32_t>(static_cast<boost::int32_t>(str.at(ix)) - static_cast<boost::int32_t>(0x30)) == static_cast<boost::int32_t>(9))
1889                {
1890                   // Increment up to the next order and adjust exponent.
1891                   str.at(ix) = static_cast<char>('1');
1892                   ++my_exp;
1893                }
1894                else
1895                {
1896                   // Round up this digit.
1897                   ++str.at(ix);
1898                }
1899             }
1900             else
1901             {
1902                // Round up the last digit.
1903                ++str[ix];
1904             }
1905          }
1906       }
1907    }
1908
1909    if(have_leading_zeros)
1910    {
1911       // We need to take the zeros back out again, and correct the exponent
1912       // if we rounded up:
1913       if(str[std::string::size_type(number_of_digits - 1)] != '0')
1914       {
1915          ++my_exp;
1916          str.erase(0, std::string::size_type(number_of_digits - 1));
1917       }
1918       else
1919          str.erase(0, std::string::size_type(number_of_digits));
1920    }
1921
1922    if(isneg())
1923       str.insert(static_cast<std::string::size_type>(0), 1, '-');
1924
1925    boost::multiprecision::detail::format_float_string(str, my_exp, org_digits, f, this->iszero());
1926    return str;
1927 }
1928
1929 template <unsigned Digits10, class ExponentType, class Allocator>
1930 bool cpp_dec_float<Digits10, ExponentType, Allocator>::rd_string(const char* const s)
1931 {
1932 #ifndef BOOST_NO_EXCEPTIONS
1933    try{
1934 #endif
1935
1936    std::string str(s);
1937
1938    // TBD: Using several regular expressions may significantly reduce
1939    // the code complexity (and perhaps the run-time) of rd_string().
1940
1941    // Get a possible exponent and remove it.
1942    exp = static_cast<ExponentType>(0);
1943
1944    std::size_t pos;
1945
1946    if( ((pos = str.find('e')) != std::string::npos)
1947       || ((pos = str.find('E')) != std::string::npos)
1948       )
1949    {
1950       // Remove the exponent part from the string.
1951       exp = boost::lexical_cast<ExponentType>(static_cast<const char*>(str.c_str() + (pos + 1u)));
1952       str = str.substr(static_cast<std::size_t>(0u), pos);
1953    }
1954
1955    // Get a possible +/- sign and remove it.
1956    neg = false;
1957
1958    if(str.size())
1959    {
1960       if(str[0] == '-')
1961       {
1962          neg = true;
1963          str.erase(0, 1);
1964       }
1965       else if(str[0] == '+')
1966       {
1967          str.erase(0, 1);
1968       }
1969    }
1970    //
1971    // Special cases for infinities and NaN's:
1972    //
1973    if((str == "inf") || (str == "INF") || (str == "infinity") || (str == "INFINITY"))
1974    {
1975       if(neg)
1976       {
1977          *this = this->inf();
1978          this->negate();
1979       }
1980       else
1981          *this = this->inf();
1982       return true;
1983    }
1984    if((str.size() >= 3) && ((str.substr(0, 3) == "nan") || (str.substr(0, 3) == "NAN") || (str.substr(0, 3) == "NaN")))
1985    {
1986       *this = this->nan();
1987       return true;
1988    }
1989
1990    // Remove the leading zeros for all input types.
1991    const std::string::iterator fwd_it_leading_zero = std::find_if(str.begin(), str.end(), char_is_nonzero_predicate);
1992
1993    if(fwd_it_leading_zero != str.begin())
1994    {
1995       if(fwd_it_leading_zero == str.end())
1996       {
1997          // The string contains nothing but leading zeros.
1998          // This string represents zero.
1999          operator=(zero());
2000          return true;
2001       }
2002       else
2003       {
2004          str.erase(str.begin(), fwd_it_leading_zero);
2005       }
2006    }
2007
2008    // Put the input string into the standard cpp_dec_float<Digits10, ExponentType, Allocator> input form
2009    // aaa.bbbbE+/-n, where aaa has 1...cpp_dec_float_elem_digits10, bbbb has an
2010    // even multiple of cpp_dec_float_elem_digits10 which are possibly zero padded
2011    // on the right-end, and n is a signed 64-bit integer which is an
2012    // even multiple of cpp_dec_float_elem_digits10.
2013
2014    // Find a possible decimal point.
2015    pos = str.find(static_cast<char>('.'));
2016
2017    if(pos != std::string::npos)
2018    {
2019       // Remove all trailing insignificant zeros.
2020       const std::string::const_reverse_iterator rit_non_zero = std::find_if(str.rbegin(), str.rend(), char_is_nonzero_predicate);
2021
2022       if(rit_non_zero != static_cast<std::string::const_reverse_iterator>(str.rbegin()))
2023       {
2024          const std::string::size_type ofs = str.length() - std::distance<std::string::const_reverse_iterator>(str.rbegin(), rit_non_zero);
2025          str.erase(str.begin() + ofs, str.end());
2026       }
2027
2028       // Check if the input is identically zero.
2029       if(str == std::string("."))
2030       {
2031          operator=(zero());
2032          return true;
2033       }
2034
2035       // Remove leading significant zeros just after the decimal point
2036       // and adjust the exponent accordingly.
2037       // Note that the while-loop operates only on strings of the form ".000abcd..."
2038       // and peels away the zeros just after the decimal point.
2039       if(str.at(static_cast<std::size_t>(0u)) == static_cast<char>('.'))
2040       {
2041          const std::string::iterator it_non_zero = std::find_if(str.begin() + 1u, str.end(), char_is_nonzero_predicate);
2042
2043          std::size_t delta_exp = static_cast<std::size_t>(0u);
2044
2045          if(str.at(static_cast<std::size_t>(1u)) == static_cast<char>('0'))
2046          {
2047             delta_exp = std::distance<std::string::const_iterator>(str.begin() + 1u, it_non_zero);
2048          }
2049
2050          // Bring one single digit into the mantissa and adjust the exponent accordingly.
2051          str.erase(str.begin(), it_non_zero);
2052          str.insert(static_cast<std::string::size_type>(1u), ".");
2053          exp -= static_cast<ExponentType>(delta_exp + 1u);
2054       }
2055    }
2056    else
2057    {
2058       // Input string has no decimal point: Append decimal point.
2059       str.append(".");
2060    }
2061
2062    // Shift the decimal point such that the exponent is an even multiple of cpp_dec_float_elem_digits10.
2063    std::size_t n_shift = static_cast<std::size_t>(0u);
2064    const std::size_t n_exp_rem = static_cast<std::size_t>(exp % static_cast<ExponentType>(cpp_dec_float_elem_digits10));
2065
2066    if((exp % static_cast<ExponentType>(cpp_dec_float_elem_digits10)) != static_cast<ExponentType>(0))
2067    {
2068       n_shift = ((exp < static_cast<ExponentType>(0))
2069          ? static_cast<std::size_t>(n_exp_rem + static_cast<std::size_t>(cpp_dec_float_elem_digits10))
2070          : static_cast<std::size_t>(n_exp_rem));
2071    }
2072
2073    // Make sure that there are enough digits for the decimal point shift.
2074    pos = str.find(static_cast<char>('.'));
2075
2076    std::size_t pos_plus_one = static_cast<std::size_t>(pos + 1u);
2077
2078    if((str.length() - pos_plus_one) < n_shift)
2079    {
2080       const std::size_t sz = static_cast<std::size_t>(n_shift - (str.length() - pos_plus_one));
2081
2082       str.append(std::string(sz, static_cast<char>('0')));
2083    }
2084
2085    // Do the decimal point shift.
2086    if(n_shift != static_cast<std::size_t>(0u))
2087    {
2088       str.insert(static_cast<std::string::size_type>(pos_plus_one + n_shift), ".");
2089
2090       str.erase(pos, static_cast<std::string::size_type>(1u));
2091
2092       exp -= static_cast<ExponentType>(n_shift);
2093    }
2094
2095    // Cut the size of the mantissa to <= cpp_dec_float_elem_digits10.
2096    pos = str.find(static_cast<char>('.'));
2097    pos_plus_one = static_cast<std::size_t>(pos + 1u);
2098
2099    if(pos > static_cast<std::size_t>(cpp_dec_float_elem_digits10))
2100    {
2101       const boost::int32_t n_pos = static_cast<boost::int32_t>(pos);
2102       const boost::int32_t n_rem_is_zero = ((static_cast<boost::int32_t>(n_pos % cpp_dec_float_elem_digits10) == static_cast<boost::int32_t>(0)) ? static_cast<boost::int32_t>(1) : static_cast<boost::int32_t>(0));
2103       const boost::int32_t n = static_cast<boost::int32_t>(static_cast<boost::int32_t>(n_pos / cpp_dec_float_elem_digits10) - n_rem_is_zero);
2104
2105       str.insert(static_cast<std::size_t>(static_cast<boost::int32_t>(n_pos - static_cast<boost::int32_t>(n * cpp_dec_float_elem_digits10))), ".");
2106
2107       str.erase(pos_plus_one, static_cast<std::size_t>(1u));
2108
2109       exp += static_cast<ExponentType>(static_cast<ExponentType>(n) * static_cast<ExponentType>(cpp_dec_float_elem_digits10));
2110    }
2111
2112    // Pad the decimal part such that its value is an even
2113    // multiple of cpp_dec_float_elem_digits10.
2114    pos = str.find(static_cast<char>('.'));
2115    pos_plus_one = static_cast<std::size_t>(pos + 1u);
2116
2117    const boost::int32_t n_dec = static_cast<boost::int32_t>(static_cast<boost::int32_t>(str.length() - 1u) - static_cast<boost::int32_t>(pos));
2118    const boost::int32_t n_rem = static_cast<boost::int32_t>(n_dec % cpp_dec_float_elem_digits10);
2119
2120    boost::int32_t n_cnt = ((n_rem != static_cast<boost::int32_t>(0))
2121                              ? static_cast<boost::int32_t>(cpp_dec_float_elem_digits10 - n_rem)
2122                              : static_cast<boost::int32_t>(0));
2123
2124    if(n_cnt != static_cast<boost::int32_t>(0))
2125    {
2126       str.append(static_cast<std::size_t>(n_cnt), static_cast<char>('0'));
2127    }
2128
2129    // Truncate decimal part if it is too long.
2130    const std::size_t max_dec = static_cast<std::size_t>((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10);
2131
2132    if(static_cast<std::size_t>(str.length() - pos) > max_dec)
2133    {
2134       str = str.substr(static_cast<std::size_t>(0u),
2135          static_cast<std::size_t>(pos_plus_one + max_dec));
2136    }
2137
2138    // Now the input string has the standard cpp_dec_float<Digits10, ExponentType, Allocator> input form.
2139    // (See the comment above.)
2140
2141    // Set all the data elements to 0.
2142    std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u));
2143
2144    // Extract the data.
2145
2146    // First get the digits to the left of the decimal point...
2147    data[0u] = boost::lexical_cast<boost::uint32_t>(str.substr(static_cast<std::size_t>(0u), pos));
2148
2149    // ...then get the remaining digits to the right of the decimal point.
2150    const std::string::size_type i_end = ((str.length() - pos_plus_one) / static_cast<std::string::size_type>(cpp_dec_float_elem_digits10));
2151
2152    for(std::string::size_type i = static_cast<std::string::size_type>(0u); i < i_end; i++)
2153    {
2154       const std::string::const_iterator it = str.begin()
2155          + pos_plus_one
2156          + (i * static_cast<std::string::size_type>(cpp_dec_float_elem_digits10));
2157
2158       data[i + 1u] = boost::lexical_cast<boost::uint32_t>(std::string(it, it + static_cast<std::string::size_type>(cpp_dec_float_elem_digits10)));
2159    }
2160
2161    // Check for overflow...
2162    if(exp > cpp_dec_float_max_exp10)
2163    {
2164       const bool b_result_is_neg = neg;
2165
2166       *this = inf();
2167       if(b_result_is_neg)
2168          negate();
2169    }
2170
2171    // ...and check for underflow.
2172    if(exp <= cpp_dec_float_min_exp10)
2173    {
2174       if(exp == cpp_dec_float_min_exp10)
2175       {
2176          // Check for identity with the minimum value.
2177          cpp_dec_float<Digits10, ExponentType, Allocator> test = *this;
2178
2179          test.exp = static_cast<ExponentType>(0);
2180
2181          if(test.isone())
2182          {
2183             *this = zero();
2184          }
2185       }
2186       else
2187       {
2188          *this = zero();
2189       }
2190    }
2191
2192 #ifndef BOOST_NO_EXCEPTIONS
2193    }
2194    catch(const bad_lexical_cast&)
2195    {
2196       // Rethrow with better error message:
2197       std::string msg = "Unable to parse the string \"";
2198       msg += s;
2199       msg += "\" as a floating point value.";
2200       throw std::runtime_error(msg);
2201    }
2202 #endif
2203    return true;
2204 }
2205
2206 template <unsigned Digits10, class ExponentType, class Allocator>
2207 cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float(const double mantissa, const ExponentType exponent)
2208  : data (),
2209    exp  (static_cast<ExponentType>(0)),
2210    neg  (false),
2211    fpclass (cpp_dec_float_finite),
2212    prec_elem(cpp_dec_float_elem_number)
2213 {
2214    // Create *this cpp_dec_float<Digits10, ExponentType, Allocator> from a given mantissa and exponent.
2215    // Note: This constructor does not maintain the full precision of double.
2216
2217    const bool mantissa_is_iszero = (::fabs(mantissa) < ((std::numeric_limits<double>::min)() * (1.0 + std::numeric_limits<double>::epsilon())));
2218
2219    if(mantissa_is_iszero)
2220    {
2221       std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u));
2222       return;
2223    }
2224
2225    const bool b_neg = (mantissa < 0.0);
2226
2227    double d = ((!b_neg) ? mantissa : -mantissa);
2228    ExponentType e = exponent;
2229
2230    while(d > 10.0) { d /= 10.0; ++e; }
2231    while(d < 1.0) { d *= 10.0; --e; }
2232
2233    boost::int32_t shift = static_cast<boost::int32_t>(e % static_cast<boost::int32_t>(cpp_dec_float_elem_digits10));
2234
2235    while(static_cast<boost::int32_t>(shift-- % cpp_dec_float_elem_digits10) != static_cast<boost::int32_t>(0))
2236    {
2237       d *= 10.0;
2238       --e;
2239    }
2240
2241    exp = e;
2242    neg = b_neg;
2243
2244    std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u));
2245
2246    static const boost::int32_t digit_ratio = static_cast<boost::int32_t>(static_cast<boost::int32_t>(std::numeric_limits<double>::digits10) / static_cast<boost::int32_t>(cpp_dec_float_elem_digits10));
2247    static const boost::int32_t digit_loops = static_cast<boost::int32_t>(digit_ratio + static_cast<boost::int32_t>(2));
2248
2249    for(boost::int32_t i = static_cast<boost::int32_t>(0); i < digit_loops; i++)
2250    {
2251       boost::uint32_t n = static_cast<boost::uint32_t>(static_cast<boost::uint64_t>(d));
2252       data[i] = static_cast<boost::uint32_t>(n);
2253       d -= static_cast<double>(n);
2254       d *= static_cast<double>(cpp_dec_float_elem_mask);
2255    }
2256 }
2257
2258 template <unsigned Digits10, class ExponentType, class Allocator>
2259 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator= (long double a)
2260 {
2261    // Christopher Kormanyos's original code used a cast to boost::long_long_type here, but that fails
2262    // when long double has more digits than a boost::long_long_type.
2263    using std::frexp;
2264    using std::ldexp;
2265    using std::floor;
2266
2267    if(a == 0)
2268       return *this = zero();
2269
2270    if(a == 1)
2271       return *this = one();
2272
2273    if((boost::math::isinf)(a))
2274    {
2275       *this = inf();
2276       if(a < 0)
2277          this->negate();
2278       return *this;
2279    }
2280
2281    if((boost::math::isnan)(a))
2282       return *this = nan();
2283
2284    int e;
2285    long double f, term;
2286    *this = zero();
2287
2288    f = frexp(a, &e);
2289    // See https://svn.boost.org/trac/boost/ticket/10924 for an example of why this may go wrong:
2290    BOOST_ASSERT((boost::math::isfinite)(f));
2291
2292    static const int shift = std::numeric_limits<int>::digits - 1;
2293
2294    while(f)
2295    {
2296       // extract int sized bits from f:
2297       f = ldexp(f, shift);
2298       BOOST_ASSERT((boost::math::isfinite)(f));
2299       term = floor(f);
2300       e -= shift;
2301       *this *= pow2(shift);
2302       if(term > 0)
2303          add_unsigned_long_long(static_cast<unsigned>(term));
2304       else
2305          sub_unsigned_long_long(static_cast<unsigned>(-term));
2306       f -= term;
2307    }
2308
2309    if(e != 0)
2310       *this *= pow2(e);
2311
2312    return *this;
2313 }
2314
2315 template <unsigned Digits10, class ExponentType, class Allocator>
2316 void cpp_dec_float<Digits10, ExponentType, Allocator>::from_unsigned_long_long(const boost::ulong_long_type u)
2317 {
2318    std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u));
2319
2320    exp = static_cast<ExponentType>(0);
2321    neg = false;
2322    fpclass = cpp_dec_float_finite;
2323    prec_elem = cpp_dec_float_elem_number;
2324
2325    if(u == 0)
2326    {
2327       return;
2328    }
2329
2330    std::size_t i =static_cast<std::size_t>(0u);
2331
2332    boost::ulong_long_type uu = u;
2333
2334    boost::uint32_t temp[(std::numeric_limits<boost::ulong_long_type>::digits10 / static_cast<int>(cpp_dec_float_elem_digits10)) + 3] = { static_cast<boost::uint32_t>(0u) };
2335
2336    while(uu != static_cast<boost::ulong_long_type>(0u))
2337    {
2338       temp[i] = static_cast<boost::uint32_t>(uu % static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask));
2339       uu = static_cast<boost::ulong_long_type>(uu / static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask));
2340       ++i;
2341    }
2342
2343    if(i > static_cast<std::size_t>(1u))
2344    {
2345       exp += static_cast<ExponentType>((i - 1u) * static_cast<std::size_t>(cpp_dec_float_elem_digits10));
2346    }
2347
2348    std::reverse(temp, temp + i);
2349    std::copy(temp, temp + (std::min)(i, static_cast<std::size_t>(cpp_dec_float_elem_number)), data.begin());
2350 }
2351
2352 template <unsigned Digits10, class ExponentType, class Allocator>
2353 boost::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p)
2354 {
2355    //
2356    // There is a limit on how many limbs this algorithm can handle without dropping digits
2357    // due to overflow in the carry, it is:
2358    //
2359    // FLOOR( (2^64 - 1) / (10^8 * 10^8) ) == 1844
2360    //
2361    BOOST_STATIC_ASSERT_MSG(cpp_dec_float_elem_number < 1800, "Too many limbs in the data type for the multiplication algorithm - unsupported precision in cpp_dec_float.");
2362
2363    boost::uint64_t carry = static_cast<boost::uint64_t>(0u);
2364
2365    for(boost::int32_t j = static_cast<boost::int32_t>(p - 1u); j >= static_cast<boost::int32_t>(0); j--)
2366    {
2367      boost::uint64_t sum = carry;
2368
2369      for(boost::int32_t i = j; i >= static_cast<boost::int32_t>(0); i--)
2370      {
2371        sum += static_cast<boost::uint64_t>(u[j - i] * static_cast<boost::uint64_t>(v[i]));
2372      }
2373
2374      u[j] = static_cast<boost::uint32_t>(sum % static_cast<boost::uint32_t>(cpp_dec_float_elem_mask));
2375      carry = static_cast<boost::uint64_t>(sum / static_cast<boost::uint32_t>(cpp_dec_float_elem_mask));
2376    }
2377
2378    return static_cast<boost::uint32_t>(carry);
2379 }
2380
2381 template <unsigned Digits10, class ExponentType, class Allocator>
2382 boost::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p)
2383 {
2384    boost::uint64_t carry = static_cast<boost::uint64_t>(0u);
2385
2386    // Multiplication loop.
2387    for(boost::int32_t j = p - 1; j >= static_cast<boost::int32_t>(0); j--)
2388    {
2389       const boost::uint64_t t = static_cast<boost::uint64_t>(carry + static_cast<boost::uint64_t>(u[j] * static_cast<boost::uint64_t>(n)));
2390       carry = static_cast<boost::uint64_t>(t / static_cast<boost::uint32_t>(cpp_dec_float_elem_mask));
2391       u[j] = static_cast<boost::uint32_t>(t - static_cast<boost::uint64_t>(static_cast<boost::uint32_t>(cpp_dec_float_elem_mask) * static_cast<boost::uint64_t>(carry)));
2392    }
2393
2394    return static_cast<boost::uint32_t>(carry);
2395 }
2396
2397 template <unsigned Digits10, class ExponentType, class Allocator>
2398 boost::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p)
2399 {
2400    boost::uint64_t prev = static_cast<boost::uint64_t>(0u);
2401
2402    for(boost::int32_t j = static_cast<boost::int32_t>(0); j < p; j++)
2403    {
2404       const boost::uint64_t t = static_cast<boost::uint64_t>(u[j] + static_cast<boost::uint64_t>(prev * static_cast<boost::uint32_t>(cpp_dec_float_elem_mask)));
2405       u[j] = static_cast<boost::uint32_t>(t / n);
2406       prev = static_cast<boost::uint64_t>(t - static_cast<boost::uint64_t>(n * static_cast<boost::uint64_t>(u[j])));
2407    }
2408
2409    return static_cast<boost::uint32_t>(prev);
2410 }
2411
2412 template <unsigned Digits10, class ExponentType, class Allocator>
2413 cpp_dec_float<Digits10, ExponentType, Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(const boost::long_long_type p)
2414 {
2415    // Create a static const table of p^2 for -128 < p < +128.
2416    // Note: The size of this table must be odd-numbered and
2417    // symmetric about 0.
2418    init.do_nothing();
2419    static const boost::array<cpp_dec_float<Digits10, ExponentType, Allocator>, 255u> p2_data =
2420    {{
2421        cpp_dec_float("5.877471754111437539843682686111228389093327783860437607543758531392086297273635864257812500000000000e-39"),
2422        cpp_dec_float("1.175494350822287507968736537222245677818665556772087521508751706278417259454727172851562500000000000e-38"),
2423        cpp_dec_float("2.350988701644575015937473074444491355637331113544175043017503412556834518909454345703125000000000000e-38"),
2424        cpp_dec_float("4.701977403289150031874946148888982711274662227088350086035006825113669037818908691406250000000000000e-38"),
2425        cpp_dec_float("9.403954806578300063749892297777965422549324454176700172070013650227338075637817382812500000000000000e-38"),
2426        cpp_dec_float("1.880790961315660012749978459555593084509864890835340034414002730045467615127563476562500000000000000e-37"),
2427        cpp_dec_float("3.761581922631320025499956919111186169019729781670680068828005460090935230255126953125000000000000000e-37"),
2428        cpp_dec_float("7.523163845262640050999913838222372338039459563341360137656010920181870460510253906250000000000000000e-37"),
2429        cpp_dec_float("1.504632769052528010199982767644474467607891912668272027531202184036374092102050781250000000000000000e-36"),
2430        cpp_dec_float("3.009265538105056020399965535288948935215783825336544055062404368072748184204101562500000000000000000e-36"),
2431        cpp_dec_float("6.018531076210112040799931070577897870431567650673088110124808736145496368408203125000000000000000000e-36"),
2432        cpp_dec_float("1.203706215242022408159986214115579574086313530134617622024961747229099273681640625000000000000000000e-35"),
2433        cpp_dec_float("2.407412430484044816319972428231159148172627060269235244049923494458198547363281250000000000000000000e-35"),
2434        cpp_dec_float("4.814824860968089632639944856462318296345254120538470488099846988916397094726562500000000000000000000e-35"),
2435        cpp_dec_float("9.629649721936179265279889712924636592690508241076940976199693977832794189453125000000000000000000000e-35"),
2436        cpp_dec_float("1.925929944387235853055977942584927318538101648215388195239938795566558837890625000000000000000000000e-34"),
2437        cpp_dec_float("3.851859888774471706111955885169854637076203296430776390479877591133117675781250000000000000000000000e-34"),
2438        cpp_dec_float("7.703719777548943412223911770339709274152406592861552780959755182266235351562500000000000000000000000e-34"),
2439        cpp_dec_float("1.540743955509788682444782354067941854830481318572310556191951036453247070312500000000000000000000000e-33"),
2440        cpp_dec_float("3.081487911019577364889564708135883709660962637144621112383902072906494140625000000000000000000000000e-33"),
2441        cpp_dec_float("6.162975822039154729779129416271767419321925274289242224767804145812988281250000000000000000000000000e-33"),
2442        cpp_dec_float("1.232595164407830945955825883254353483864385054857848444953560829162597656250000000000000000000000000e-32"),
2443        cpp_dec_float("2.465190328815661891911651766508706967728770109715696889907121658325195312500000000000000000000000000e-32"),
2444        cpp_dec_float("4.930380657631323783823303533017413935457540219431393779814243316650390625000000000000000000000000000e-32"),
2445        cpp_dec_float("9.860761315262647567646607066034827870915080438862787559628486633300781250000000000000000000000000000e-32"),
2446        cpp_dec_float("1.972152263052529513529321413206965574183016087772557511925697326660156250000000000000000000000000000e-31"),
2447        cpp_dec_float("3.944304526105059027058642826413931148366032175545115023851394653320312500000000000000000000000000000e-31"),
2448        cpp_dec_float("7.888609052210118054117285652827862296732064351090230047702789306640625000000000000000000000000000000e-31"),
2449        cpp_dec_float("1.577721810442023610823457130565572459346412870218046009540557861328125000000000000000000000000000000e-30"),
2450        cpp_dec_float("3.155443620884047221646914261131144918692825740436092019081115722656250000000000000000000000000000000e-30"),
2451        cpp_dec_float("6.310887241768094443293828522262289837385651480872184038162231445312500000000000000000000000000000000e-30"),
2452        cpp_dec_float("1.262177448353618888658765704452457967477130296174436807632446289062500000000000000000000000000000000e-29"),
2453        cpp_dec_float("2.524354896707237777317531408904915934954260592348873615264892578125000000000000000000000000000000000e-29"),
2454        cpp_dec_float("5.048709793414475554635062817809831869908521184697747230529785156250000000000000000000000000000000000e-29"),
2455        cpp_dec_float("1.009741958682895110927012563561966373981704236939549446105957031250000000000000000000000000000000000e-28"),
2456        cpp_dec_float("2.019483917365790221854025127123932747963408473879098892211914062500000000000000000000000000000000000e-28"),
2457        cpp_dec_float("4.038967834731580443708050254247865495926816947758197784423828125000000000000000000000000000000000000e-28"),
2458        cpp_dec_float("8.077935669463160887416100508495730991853633895516395568847656250000000000000000000000000000000000000e-28"),
2459        cpp_dec_float("1.615587133892632177483220101699146198370726779103279113769531250000000000000000000000000000000000000e-27"),
2460        cpp_dec_float("3.231174267785264354966440203398292396741453558206558227539062500000000000000000000000000000000000000e-27"),
2461        cpp_dec_float("6.462348535570528709932880406796584793482907116413116455078125000000000000000000000000000000000000000e-27"),
2462        cpp_dec_float("1.292469707114105741986576081359316958696581423282623291015625000000000000000000000000000000000000000e-26"),
2463        cpp_dec_float("2.584939414228211483973152162718633917393162846565246582031250000000000000000000000000000000000000000e-26"),
2464        cpp_dec_float("5.169878828456422967946304325437267834786325693130493164062500000000000000000000000000000000000000000e-26"),
2465        cpp_dec_float("1.033975765691284593589260865087453566957265138626098632812500000000000000000000000000000000000000000e-25"),
2466        cpp_dec_float("2.067951531382569187178521730174907133914530277252197265625000000000000000000000000000000000000000000e-25"),
2467        cpp_dec_float("4.135903062765138374357043460349814267829060554504394531250000000000000000000000000000000000000000000e-25"),
2468        cpp_dec_float("8.271806125530276748714086920699628535658121109008789062500000000000000000000000000000000000000000000e-25"),
2469        cpp_dec_float("1.654361225106055349742817384139925707131624221801757812500000000000000000000000000000000000000000000e-24"),
2470        cpp_dec_float("3.308722450212110699485634768279851414263248443603515625000000000000000000000000000000000000000000000e-24"),
2471        cpp_dec_float("6.617444900424221398971269536559702828526496887207031250000000000000000000000000000000000000000000000e-24"),
2472        cpp_dec_float("1.323488980084844279794253907311940565705299377441406250000000000000000000000000000000000000000000000e-23"),
2473        cpp_dec_float("2.646977960169688559588507814623881131410598754882812500000000000000000000000000000000000000000000000e-23"),
2474        cpp_dec_float("5.293955920339377119177015629247762262821197509765625000000000000000000000000000000000000000000000000e-23"),
2475        cpp_dec_float("1.058791184067875423835403125849552452564239501953125000000000000000000000000000000000000000000000000e-22"),
2476        cpp_dec_float("2.117582368135750847670806251699104905128479003906250000000000000000000000000000000000000000000000000e-22"),
2477        cpp_dec_float("4.235164736271501695341612503398209810256958007812500000000000000000000000000000000000000000000000000e-22"),
2478        cpp_dec_float("8.470329472543003390683225006796419620513916015625000000000000000000000000000000000000000000000000000e-22"),
2479        cpp_dec_float("1.694065894508600678136645001359283924102783203125000000000000000000000000000000000000000000000000000e-21"),
2480        cpp_dec_float("3.388131789017201356273290002718567848205566406250000000000000000000000000000000000000000000000000000e-21"),
2481        cpp_dec_float("6.776263578034402712546580005437135696411132812500000000000000000000000000000000000000000000000000000e-21"),
2482        cpp_dec_float("1.355252715606880542509316001087427139282226562500000000000000000000000000000000000000000000000000000e-20"),
2483        cpp_dec_float("2.710505431213761085018632002174854278564453125000000000000000000000000000000000000000000000000000000e-20"),
2484        cpp_dec_float("5.421010862427522170037264004349708557128906250000000000000000000000000000000000000000000000000000000e-20"),
2485        cpp_dec_float("1.084202172485504434007452800869941711425781250000000000000000000000000000000000000000000000000000000e-19"),
2486        cpp_dec_float("2.168404344971008868014905601739883422851562500000000000000000000000000000000000000000000000000000000e-19"),
2487        cpp_dec_float("4.336808689942017736029811203479766845703125000000000000000000000000000000000000000000000000000000000e-19"),
2488        cpp_dec_float("8.673617379884035472059622406959533691406250000000000000000000000000000000000000000000000000000000000e-19"),
2489        cpp_dec_float("1.734723475976807094411924481391906738281250000000000000000000000000000000000000000000000000000000000e-18"),
2490        cpp_dec_float("3.469446951953614188823848962783813476562500000000000000000000000000000000000000000000000000000000000e-18"),
2491        cpp_dec_float("6.938893903907228377647697925567626953125000000000000000000000000000000000000000000000000000000000000e-18"),
2492        cpp_dec_float("1.387778780781445675529539585113525390625000000000000000000000000000000000000000000000000000000000000e-17"),
2493        cpp_dec_float("2.775557561562891351059079170227050781250000000000000000000000000000000000000000000000000000000000000e-17"),
2494        cpp_dec_float("5.551115123125782702118158340454101562500000000000000000000000000000000000000000000000000000000000000e-17"),
2495        cpp_dec_float("1.110223024625156540423631668090820312500000000000000000000000000000000000000000000000000000000000000e-16"),
2496        cpp_dec_float("2.220446049250313080847263336181640625000000000000000000000000000000000000000000000000000000000000000e-16"),
2497        cpp_dec_float("4.440892098500626161694526672363281250000000000000000000000000000000000000000000000000000000000000000e-16"),
2498        cpp_dec_float("8.881784197001252323389053344726562500000000000000000000000000000000000000000000000000000000000000000e-16"),
2499        cpp_dec_float("1.776356839400250464677810668945312500000000000000000000000000000000000000000000000000000000000000000e-15"),
2500        cpp_dec_float("3.552713678800500929355621337890625000000000000000000000000000000000000000000000000000000000000000000e-15"),
2501        cpp_dec_float("7.105427357601001858711242675781250000000000000000000000000000000000000000000000000000000000000000000e-15"),
2502        cpp_dec_float("1.421085471520200371742248535156250000000000000000000000000000000000000000000000000000000000000000000e-14"),
2503        cpp_dec_float("2.842170943040400743484497070312500000000000000000000000000000000000000000000000000000000000000000000e-14"),
2504        cpp_dec_float("5.684341886080801486968994140625000000000000000000000000000000000000000000000000000000000000000000000e-14"),
2505        cpp_dec_float("1.136868377216160297393798828125000000000000000000000000000000000000000000000000000000000000000000000e-13"),
2506        cpp_dec_float("2.273736754432320594787597656250000000000000000000000000000000000000000000000000000000000000000000000e-13"),
2507        cpp_dec_float("4.547473508864641189575195312500000000000000000000000000000000000000000000000000000000000000000000000e-13"),
2508        cpp_dec_float("9.094947017729282379150390625000000000000000000000000000000000000000000000000000000000000000000000000e-13"),
2509        cpp_dec_float("1.818989403545856475830078125000000000000000000000000000000000000000000000000000000000000000000000000e-12"),
2510        cpp_dec_float("3.637978807091712951660156250000000000000000000000000000000000000000000000000000000000000000000000000e-12"),
2511        cpp_dec_float("7.275957614183425903320312500000000000000000000000000000000000000000000000000000000000000000000000000e-12"),
2512        cpp_dec_float("1.455191522836685180664062500000000000000000000000000000000000000000000000000000000000000000000000000e-11"),
2513        cpp_dec_float("2.910383045673370361328125000000000000000000000000000000000000000000000000000000000000000000000000000e-11"),
2514        cpp_dec_float("5.820766091346740722656250000000000000000000000000000000000000000000000000000000000000000000000000000e-11"),
2515        cpp_dec_float("1.164153218269348144531250000000000000000000000000000000000000000000000000000000000000000000000000000e-10"),
2516        cpp_dec_float("2.328306436538696289062500000000000000000000000000000000000000000000000000000000000000000000000000000e-10"),
2517        cpp_dec_float("4.656612873077392578125000000000000000000000000000000000000000000000000000000000000000000000000000000e-10"),
2518        cpp_dec_float("9.313225746154785156250000000000000000000000000000000000000000000000000000000000000000000000000000000e-10"),
2519        cpp_dec_float("1.862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"),
2520        cpp_dec_float("3.725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"),
2521        cpp_dec_float("7.450580596923828125000000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"),
2522        cpp_dec_float("1.490116119384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"),
2523        cpp_dec_float("2.980232238769531250000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"),
2524        cpp_dec_float("5.960464477539062500000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"),
2525        cpp_dec_float("1.192092895507812500000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"),
2526        cpp_dec_float("2.384185791015625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"),
2527        cpp_dec_float("4.768371582031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"),
2528        cpp_dec_float("9.536743164062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"),
2529        cpp_dec_float("1.907348632812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"),
2530        cpp_dec_float("3.814697265625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"),
2531        cpp_dec_float("7.629394531250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"),
2532        cpp_dec_float("0.000015258789062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2533        cpp_dec_float("0.000030517578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2534        cpp_dec_float("0.000061035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2535        cpp_dec_float("0.000122070312500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2536        cpp_dec_float("0.000244140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2537        cpp_dec_float("0.000488281250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2538        cpp_dec_float("0.000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2539        cpp_dec_float("0.001953125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2540        cpp_dec_float("0.003906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2541        cpp_dec_float("0.007812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2542        cpp_dec_float("0.01562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2543        cpp_dec_float("0.03125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2544        cpp_dec_float("0.06250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2545        cpp_dec_float("0.125"),
2546        cpp_dec_float("0.25"),
2547        cpp_dec_float("0.5"),
2548        one(),
2549        two(),
2550        cpp_dec_float(static_cast<boost::ulong_long_type>(4)),
2551        cpp_dec_float(static_cast<boost::ulong_long_type>(8)),
2552        cpp_dec_float(static_cast<boost::ulong_long_type>(16)),
2553        cpp_dec_float(static_cast<boost::ulong_long_type>(32)),
2554        cpp_dec_float(static_cast<boost::ulong_long_type>(64)),
2555        cpp_dec_float(static_cast<boost::ulong_long_type>(128)),
2556        cpp_dec_float(static_cast<boost::ulong_long_type>(256)),
2557        cpp_dec_float(static_cast<boost::ulong_long_type>(512)),
2558        cpp_dec_float(static_cast<boost::ulong_long_type>(1024)),
2559        cpp_dec_float(static_cast<boost::ulong_long_type>(2048)),
2560        cpp_dec_float(static_cast<boost::ulong_long_type>(4096)),
2561        cpp_dec_float(static_cast<boost::ulong_long_type>(8192)),
2562        cpp_dec_float(static_cast<boost::ulong_long_type>(16384)),
2563        cpp_dec_float(static_cast<boost::ulong_long_type>(32768)),
2564        cpp_dec_float(static_cast<boost::ulong_long_type>(65536)),
2565        cpp_dec_float(static_cast<boost::ulong_long_type>(131072)),
2566        cpp_dec_float(static_cast<boost::ulong_long_type>(262144)),
2567        cpp_dec_float(static_cast<boost::ulong_long_type>(524288)),
2568        cpp_dec_float(static_cast<boost::uint64_t>(1uL << 20u)),
2569        cpp_dec_float(static_cast<boost::uint64_t>(1uL << 21u)),
2570        cpp_dec_float(static_cast<boost::uint64_t>(1uL << 22u)),
2571        cpp_dec_float(static_cast<boost::uint64_t>(1uL << 23u)),
2572        cpp_dec_float(static_cast<boost::uint64_t>(1uL << 24u)),
2573        cpp_dec_float(static_cast<boost::uint64_t>(1uL << 25u)),
2574        cpp_dec_float(static_cast<boost::uint64_t>(1uL << 26u)),
2575        cpp_dec_float(static_cast<boost::uint64_t>(1uL << 27u)),
2576        cpp_dec_float(static_cast<boost::uint64_t>(1uL << 28u)),
2577        cpp_dec_float(static_cast<boost::uint64_t>(1uL << 29u)),
2578        cpp_dec_float(static_cast<boost::uint64_t>(1uL << 30u)),
2579        cpp_dec_float(static_cast<boost::uint64_t>(1uL << 31u)),
2580        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 32u)),
2581        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 33u)),
2582        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 34u)),
2583        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 35u)),
2584        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 36u)),
2585        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 37u)),
2586        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 38u)),
2587        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 39u)),
2588        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 40u)),
2589        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 41u)),
2590        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 42u)),
2591        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 43u)),
2592        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 44u)),
2593        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 45u)),
2594        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 46u)),
2595        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 47u)),
2596        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 48u)),
2597        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 49u)),
2598        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 50u)),
2599        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 51u)),
2600        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 52u)),
2601        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 53u)),
2602        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 54u)),
2603        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 55u)),
2604        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 56u)),
2605        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 57u)),
2606        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 58u)),
2607        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 59u)),
2608        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 60u)),
2609        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 61u)),
2610        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 62u)),
2611        cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 63u)),
2612        cpp_dec_float("1.844674407370955161600000000000000000000000000000000000000000000000000000000000000000000000000000000e19"),
2613        cpp_dec_float("3.689348814741910323200000000000000000000000000000000000000000000000000000000000000000000000000000000e19"),
2614        cpp_dec_float("7.378697629483820646400000000000000000000000000000000000000000000000000000000000000000000000000000000e19"),
2615        cpp_dec_float("1.475739525896764129280000000000000000000000000000000000000000000000000000000000000000000000000000000e20"),
2616        cpp_dec_float("2.951479051793528258560000000000000000000000000000000000000000000000000000000000000000000000000000000e20"),
2617        cpp_dec_float("5.902958103587056517120000000000000000000000000000000000000000000000000000000000000000000000000000000e20"),
2618        cpp_dec_float("1.180591620717411303424000000000000000000000000000000000000000000000000000000000000000000000000000000e21"),
2619        cpp_dec_float("2.361183241434822606848000000000000000000000000000000000000000000000000000000000000000000000000000000e21"),
2620        cpp_dec_float("4.722366482869645213696000000000000000000000000000000000000000000000000000000000000000000000000000000e21"),
2621        cpp_dec_float("9.444732965739290427392000000000000000000000000000000000000000000000000000000000000000000000000000000e21"),
2622        cpp_dec_float("1.888946593147858085478400000000000000000000000000000000000000000000000000000000000000000000000000000e22"),
2623        cpp_dec_float("3.777893186295716170956800000000000000000000000000000000000000000000000000000000000000000000000000000e22"),
2624        cpp_dec_float("7.555786372591432341913600000000000000000000000000000000000000000000000000000000000000000000000000000e22"),
2625        cpp_dec_float("1.511157274518286468382720000000000000000000000000000000000000000000000000000000000000000000000000000e23"),
2626        cpp_dec_float("3.022314549036572936765440000000000000000000000000000000000000000000000000000000000000000000000000000e23"),
2627        cpp_dec_float("6.044629098073145873530880000000000000000000000000000000000000000000000000000000000000000000000000000e23"),
2628        cpp_dec_float("1.208925819614629174706176000000000000000000000000000000000000000000000000000000000000000000000000000e24"),
2629        cpp_dec_float("2.417851639229258349412352000000000000000000000000000000000000000000000000000000000000000000000000000e24"),
2630        cpp_dec_float("4.835703278458516698824704000000000000000000000000000000000000000000000000000000000000000000000000000e24"),
2631        cpp_dec_float("9.671406556917033397649408000000000000000000000000000000000000000000000000000000000000000000000000000e24"),
2632        cpp_dec_float("1.934281311383406679529881600000000000000000000000000000000000000000000000000000000000000000000000000e25"),
2633        cpp_dec_float("3.868562622766813359059763200000000000000000000000000000000000000000000000000000000000000000000000000e25"),
2634        cpp_dec_float("7.737125245533626718119526400000000000000000000000000000000000000000000000000000000000000000000000000e25"),
2635        cpp_dec_float("1.547425049106725343623905280000000000000000000000000000000000000000000000000000000000000000000000000e26"),
2636        cpp_dec_float("3.094850098213450687247810560000000000000000000000000000000000000000000000000000000000000000000000000e26"),
2637        cpp_dec_float("6.189700196426901374495621120000000000000000000000000000000000000000000000000000000000000000000000000e26"),
2638        cpp_dec_float("1.237940039285380274899124224000000000000000000000000000000000000000000000000000000000000000000000000e27"),
2639        cpp_dec_float("2.475880078570760549798248448000000000000000000000000000000000000000000000000000000000000000000000000e27"),
2640        cpp_dec_float("4.951760157141521099596496896000000000000000000000000000000000000000000000000000000000000000000000000e27"),
2641        cpp_dec_float("9.903520314283042199192993792000000000000000000000000000000000000000000000000000000000000000000000000e27"),
2642        cpp_dec_float("1.980704062856608439838598758400000000000000000000000000000000000000000000000000000000000000000000000e28"),
2643        cpp_dec_float("3.961408125713216879677197516800000000000000000000000000000000000000000000000000000000000000000000000e28"),
2644        cpp_dec_float("7.922816251426433759354395033600000000000000000000000000000000000000000000000000000000000000000000000e28"),
2645        cpp_dec_float("1.584563250285286751870879006720000000000000000000000000000000000000000000000000000000000000000000000e29"),
2646        cpp_dec_float("3.169126500570573503741758013440000000000000000000000000000000000000000000000000000000000000000000000e29"),
2647        cpp_dec_float("6.338253001141147007483516026880000000000000000000000000000000000000000000000000000000000000000000000e29"),
2648        cpp_dec_float("1.267650600228229401496703205376000000000000000000000000000000000000000000000000000000000000000000000e30"),
2649        cpp_dec_float("2.535301200456458802993406410752000000000000000000000000000000000000000000000000000000000000000000000e30"),
2650        cpp_dec_float("5.070602400912917605986812821504000000000000000000000000000000000000000000000000000000000000000000000e30"),
2651        cpp_dec_float("1.014120480182583521197362564300800000000000000000000000000000000000000000000000000000000000000000000e31"),
2652        cpp_dec_float("2.028240960365167042394725128601600000000000000000000000000000000000000000000000000000000000000000000e31"),
2653        cpp_dec_float("4.056481920730334084789450257203200000000000000000000000000000000000000000000000000000000000000000000e31"),
2654        cpp_dec_float("8.112963841460668169578900514406400000000000000000000000000000000000000000000000000000000000000000000e31"),
2655        cpp_dec_float("1.622592768292133633915780102881280000000000000000000000000000000000000000000000000000000000000000000e32"),
2656        cpp_dec_float("3.245185536584267267831560205762560000000000000000000000000000000000000000000000000000000000000000000e32"),
2657        cpp_dec_float("6.490371073168534535663120411525120000000000000000000000000000000000000000000000000000000000000000000e32"),
2658        cpp_dec_float("1.298074214633706907132624082305024000000000000000000000000000000000000000000000000000000000000000000e33"),
2659        cpp_dec_float("2.596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000e33"),
2660        cpp_dec_float("5.192296858534827628530496329220096000000000000000000000000000000000000000000000000000000000000000000e33"),
2661        cpp_dec_float("1.038459371706965525706099265844019200000000000000000000000000000000000000000000000000000000000000000e34"),
2662        cpp_dec_float("2.076918743413931051412198531688038400000000000000000000000000000000000000000000000000000000000000000e34"),
2663        cpp_dec_float("4.153837486827862102824397063376076800000000000000000000000000000000000000000000000000000000000000000e34"),
2664        cpp_dec_float("8.307674973655724205648794126752153600000000000000000000000000000000000000000000000000000000000000000e34"),
2665        cpp_dec_float("1.661534994731144841129758825350430720000000000000000000000000000000000000000000000000000000000000000e35"),
2666        cpp_dec_float("3.323069989462289682259517650700861440000000000000000000000000000000000000000000000000000000000000000e35"),
2667        cpp_dec_float("6.646139978924579364519035301401722880000000000000000000000000000000000000000000000000000000000000000e35"),
2668        cpp_dec_float("1.329227995784915872903807060280344576000000000000000000000000000000000000000000000000000000000000000e36"),
2669        cpp_dec_float("2.658455991569831745807614120560689152000000000000000000000000000000000000000000000000000000000000000e36"),
2670        cpp_dec_float("5.316911983139663491615228241121378304000000000000000000000000000000000000000000000000000000000000000e36"),
2671        cpp_dec_float("1.063382396627932698323045648224275660800000000000000000000000000000000000000000000000000000000000000e37"),
2672        cpp_dec_float("2.126764793255865396646091296448551321600000000000000000000000000000000000000000000000000000000000000e37"),
2673        cpp_dec_float("4.253529586511730793292182592897102643200000000000000000000000000000000000000000000000000000000000000e37"),
2674        cpp_dec_float("8.507059173023461586584365185794205286400000000000000000000000000000000000000000000000000000000000000e37"),
2675        cpp_dec_float("1.701411834604692317316873037158841057280000000000000000000000000000000000000000000000000000000000000e38")
2676    }};
2677
2678    if((p > static_cast<boost::long_long_type>(-128)) && (p < static_cast<boost::long_long_type>(+128)))
2679    {
2680       return p2_data[static_cast<std::size_t>(p + ((p2_data.size() - 1u) / 2u))];
2681    }
2682    else
2683    {
2684       // Compute and return 2^p.
2685       if(p < static_cast<boost::long_long_type>(0))
2686       {
2687          return pow2(static_cast<boost::long_long_type>(-p)).calculate_inv();
2688       }
2689       else
2690       {
2691          cpp_dec_float<Digits10, ExponentType, Allocator> t;
2692          default_ops::detail::pow_imp(t, two(), p, mpl::true_());
2693          return t;
2694       }
2695    }
2696 }
2697
2698
2699 template <unsigned Digits10, class ExponentType, class Allocator>
2700 inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o)
2701 {
2702    result += o;
2703 }
2704 template <unsigned Digits10, class ExponentType, class Allocator>
2705 inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o)
2706 {
2707    result -= o;
2708 }
2709 template <unsigned Digits10, class ExponentType, class Allocator>
2710 inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o)
2711 {
2712    result *= o;
2713 }
2714 template <unsigned Digits10, class ExponentType, class Allocator>
2715 inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o)
2716 {
2717    result /= o;
2718 }
2719
2720 template <unsigned Digits10, class ExponentType, class Allocator>
2721 inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const boost::ulong_long_type& o)
2722 {
2723    result.add_unsigned_long_long(o);
2724 }
2725 template <unsigned Digits10, class ExponentType, class Allocator>
2726 inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const boost::ulong_long_type& o)
2727 {
2728    result.sub_unsigned_long_long(o);
2729 }
2730 template <unsigned Digits10, class ExponentType, class Allocator>
2731 inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const boost::ulong_long_type& o)
2732 {
2733    result.mul_unsigned_long_long(o);
2734 }
2735 template <unsigned Digits10, class ExponentType, class Allocator>
2736 inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const boost::ulong_long_type& o)
2737 {
2738    result.div_unsigned_long_long(o);
2739 }
2740
2741 template <unsigned Digits10, class ExponentType, class Allocator>
2742 inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, boost::long_long_type o)
2743 {
2744    if(o < 0)
2745       result.sub_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o));
2746    else
2747       result.add_unsigned_long_long(o);
2748 }
2749 template <unsigned Digits10, class ExponentType, class Allocator>
2750 inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, boost::long_long_type o)
2751 {
2752    if(o < 0)
2753       result.add_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o));
2754    else
2755       result.sub_unsigned_long_long(o);
2756 }
2757 template <unsigned Digits10, class ExponentType, class Allocator>
2758 inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, boost::long_long_type o)
2759 {
2760    if(o < 0)
2761    {
2762       result.mul_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o));
2763       result.negate();
2764    }
2765    else
2766       result.mul_unsigned_long_long(o);
2767 }
2768 template <unsigned Digits10, class ExponentType, class Allocator>
2769 inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, boost::long_long_type o)
2770 {
2771    if(o < 0)
2772    {
2773       result.div_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o));
2774       result.negate();
2775    }
2776    else
2777       result.div_unsigned_long_long(o);
2778 }
2779
2780 template <unsigned Digits10, class ExponentType, class Allocator>
2781 inline void eval_convert_to(boost::ulong_long_type* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
2782 {
2783    *result = val.extract_unsigned_long_long();
2784 }
2785 template <unsigned Digits10, class ExponentType, class Allocator>
2786 inline void eval_convert_to(boost::long_long_type* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
2787 {
2788    *result = val.extract_signed_long_long();
2789 }
2790 template <unsigned Digits10, class ExponentType, class Allocator>
2791 inline void eval_convert_to(long double* result, cpp_dec_float<Digits10, ExponentType, Allocator>& val)
2792 {
2793    *result = val.extract_long_double();
2794 }
2795
2796 //
2797 // Non member function support:
2798 //
2799 template <unsigned Digits10, class ExponentType, class Allocator>
2800 inline int eval_fpclassify(const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
2801 {
2802    if((x.isinf)())
2803       return FP_INFINITE;
2804    if((x.isnan)())
2805       return FP_NAN;
2806    if(x.iszero())
2807       return FP_ZERO;
2808    return FP_NORMAL;
2809 }
2810
2811 template <unsigned Digits10, class ExponentType, class Allocator>
2812 inline void eval_abs(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
2813 {
2814    result = x;
2815    if(x.isneg())
2816       result.negate();
2817 }
2818
2819 template <unsigned Digits10, class ExponentType, class Allocator>
2820 inline void eval_fabs(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
2821 {
2822    result = x;
2823    if(x.isneg())
2824       result.negate();
2825 }
2826
2827 template <unsigned Digits10, class ExponentType, class Allocator>
2828 inline void eval_sqrt(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
2829 {
2830    result = x;
2831    result.calculate_sqrt();
2832 }
2833
2834 template <unsigned Digits10, class ExponentType, class Allocator>
2835 inline void eval_floor(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
2836 {
2837    result = x;
2838    if(!(x.isfinite)() || x.isint())
2839    {
2840       if((x.isnan)())
2841          errno = EDOM;
2842       return;
2843    }
2844
2845    if(x.isneg())
2846       result -= cpp_dec_float<Digits10, ExponentType, Allocator>::one();
2847    result = result.extract_integer_part();
2848 }
2849
2850 template <unsigned Digits10, class ExponentType, class Allocator>
2851 inline void eval_ceil(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
2852 {
2853    result = x;
2854    if(!(x.isfinite)() || x.isint())
2855    {
2856       if((x.isnan)())
2857          errno = EDOM;
2858       return;
2859    }
2860
2861    if(!x.isneg())
2862       result += cpp_dec_float<Digits10, ExponentType, Allocator>::one();
2863    result = result.extract_integer_part();
2864 }
2865
2866 template <unsigned Digits10, class ExponentType, class Allocator>
2867 inline void eval_trunc(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
2868 {
2869    if(x.isint() || !(x.isfinite)())
2870    {
2871       result = x;
2872       if((x.isnan)())
2873          errno = EDOM;
2874       return;
2875    }
2876    result = x.extract_integer_part();
2877 }
2878
2879 template <unsigned Digits10, class ExponentType, class Allocator>
2880 inline ExponentType eval_ilogb(const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
2881 {
2882    if(val.iszero())
2883       return (std::numeric_limits<ExponentType>::min)();
2884    if((val.isinf)())
2885       return INT_MAX;
2886    if((val.isnan)())
2887 #ifdef FP_ILOGBNAN
2888       return FP_ILOGBNAN;
2889 #else
2890       return INT_MAX;
2891 #endif
2892    // Set result, to the exponent of val:
2893    return val.order();
2894 }
2895 template <unsigned Digits10, class ExponentType, class Allocator, class ArgType>
2896 inline void eval_scalbn(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val, ArgType e_)
2897 {
2898    using default_ops::eval_multiply;
2899    const ExponentType e = static_cast<ExponentType>(e_);
2900    cpp_dec_float<Digits10, ExponentType, Allocator> t(1.0, e);
2901    eval_multiply(result, val, t);
2902 }
2903
2904 template <unsigned Digits10, class ExponentType, class Allocator, class ArgType>
2905 inline void eval_ldexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, ArgType e)
2906 {
2907    const boost::long_long_type the_exp = static_cast<boost::long_long_type>(e);
2908
2909    if((the_exp > (std::numeric_limits<ExponentType>::max)()) || (the_exp < (std::numeric_limits<ExponentType>::min)()))
2910       BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Exponent value is out of range.")));
2911
2912    result = x;
2913
2914    if ((the_exp > static_cast<boost::long_long_type>(-std::numeric_limits<boost::long_long_type>::digits)) && (the_exp < static_cast<boost::long_long_type>(0)))
2915       result.div_unsigned_long_long(1ULL << static_cast<boost::long_long_type>(-the_exp));
2916    else if((the_exp < static_cast<boost::long_long_type>( std::numeric_limits<boost::long_long_type>::digits)) && (the_exp > static_cast<boost::long_long_type>(0)))
2917       result.mul_unsigned_long_long(1ULL << the_exp);
2918    else if(the_exp != static_cast<boost::long_long_type>(0))
2919       result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(e);
2920 }
2921
2922 template <unsigned Digits10, class ExponentType, class Allocator>
2923 inline void eval_frexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, ExponentType* e)
2924 {
2925    result = x;
2926
2927    if(result.iszero() || (result.isinf)() || (result.isnan)())
2928    {
2929       *e = 0;
2930       return;
2931    }
2932
2933    if(result.isneg())
2934       result.negate();
2935
2936    ExponentType t = result.order();
2937    BOOST_MP_USING_ABS
2938    if(abs(t) < ((std::numeric_limits<ExponentType>::max)() / 1000))
2939    {
2940       t *= 1000;
2941       t /= 301;
2942    }
2943    else
2944    {
2945       t /= 301;
2946       t *= 1000;
2947    }
2948
2949    result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(-t);
2950
2951    if(result.iszero() || (result.isinf)() || (result.isnan)())
2952    {
2953       // pow2 overflowed, slip the calculation up:
2954       result = x;
2955       if(result.isneg())
2956          result.negate();
2957       t /= 2;
2958       result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(-t);
2959    }
2960    BOOST_MP_USING_ABS
2961    if(abs(result.order()) > 5)
2962    {
2963       // If our first estimate doesn't get close enough then try recursion until we do:
2964       ExponentType e2;
2965       cpp_dec_float<Digits10, ExponentType, Allocator> r2;
2966       eval_frexp(r2, result, &e2);
2967       // overflow protection:
2968       if((t > 0) && (e2 > 0) && (t > (std::numeric_limits<ExponentType>::max)() - e2))
2969          BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2."));
2970       if((t < 0) && (e2 < 0) && (t < (std::numeric_limits<ExponentType>::min)() - e2))
2971          BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2."));
2972       t += e2;
2973       result = r2;
2974    }
2975
2976    while(result.compare(cpp_dec_float<Digits10, ExponentType, Allocator>::one()) >= 0)
2977    {
2978       result /= cpp_dec_float<Digits10, ExponentType, Allocator>::two();
2979       ++t;
2980    }
2981    while(result.compare(cpp_dec_float<Digits10, ExponentType, Allocator>::half()) < 0)
2982    {
2983       result *= cpp_dec_float<Digits10, ExponentType, Allocator>::two();
2984       --t;
2985    }
2986    *e = t;
2987    if(x.isneg())
2988       result.negate();
2989 }
2990
2991 template <unsigned Digits10, class ExponentType, class Allocator>
2992 inline typename disable_if<is_same<ExponentType, int> >::type eval_frexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, int* e)
2993 {
2994    ExponentType t;
2995    eval_frexp(result, x, &t);
2996    if((t > (std::numeric_limits<int>::max)()) || (t < (std::numeric_limits<int>::min)()))
2997       BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is outside the range of an int"));
2998    *e = static_cast<int>(t);
2999 }
3000
3001 template <unsigned Digits10, class ExponentType, class Allocator>
3002 inline bool eval_is_zero(const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
3003 {
3004    return val.iszero();
3005 }
3006 template <unsigned Digits10, class ExponentType, class Allocator>
3007 inline int eval_get_sign(const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
3008 {
3009    return val.iszero() ? 0 : val.isneg() ? -1 : 1;
3010 }
3011
3012 template <unsigned Digits10, class ExponentType, class Allocator>
3013 inline std::size_t hash_value(const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
3014 {
3015    return val.hash();
3016 }
3017
3018 } // namespace backends
3019
3020 using boost::multiprecision::backends::cpp_dec_float;
3021
3022
3023 typedef number<cpp_dec_float<50> > cpp_dec_float_50;
3024 typedef number<cpp_dec_float<100> > cpp_dec_float_100;
3025
3026 #ifdef BOOST_NO_SFINAE_EXPR
3027
3028 namespace detail{
3029
3030 template<unsigned D1, class E1, class A1, unsigned D2, class E2, class A2>
3031 struct is_explicitly_convertible<cpp_dec_float<D1, E1, A1>, cpp_dec_float<D2, E2, A2> > : public mpl::true_ {};
3032
3033 }
3034
3035 #endif
3036
3037
3038 }}
3039
3040 namespace std
3041 {
3042    template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3043    class numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >
3044    {
3045    public:
3046       BOOST_STATIC_CONSTEXPR bool is_specialized = true;
3047       BOOST_STATIC_CONSTEXPR bool is_signed = true;
3048       BOOST_STATIC_CONSTEXPR bool is_integer = false;
3049       BOOST_STATIC_CONSTEXPR bool is_exact = false;
3050       BOOST_STATIC_CONSTEXPR bool is_bounded = true;
3051       BOOST_STATIC_CONSTEXPR bool is_modulo = false;
3052       BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
3053       BOOST_STATIC_CONSTEXPR int digits = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10;
3054       BOOST_STATIC_CONSTEXPR int digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10;
3055       BOOST_STATIC_CONSTEXPR int max_digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_total_digits10;
3056       BOOST_STATIC_CONSTEXPR ExponentType min_exponent = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp; // Type differs from int.
3057       BOOST_STATIC_CONSTEXPR ExponentType min_exponent10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10; // Type differs from int.
3058       BOOST_STATIC_CONSTEXPR ExponentType max_exponent = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp; // Type differs from int.
3059       BOOST_STATIC_CONSTEXPR ExponentType max_exponent10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10; // Type differs from int.
3060       BOOST_STATIC_CONSTEXPR int radix = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_radix;
3061       BOOST_STATIC_CONSTEXPR std::float_round_style round_style = std::round_indeterminate;
3062       BOOST_STATIC_CONSTEXPR bool has_infinity = true;
3063       BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true;
3064       BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
3065       BOOST_STATIC_CONSTEXPR std::float_denorm_style has_denorm = std::denorm_absent;
3066       BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
3067       BOOST_STATIC_CONSTEXPR bool traps = false;
3068       BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
3069
3070       BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> (min) () { return (boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::min)(); }
3071       BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> (max) () { return (boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::max)(); }
3072       BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> lowest () { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); }
3073       BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> epsilon () { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::eps(); }
3074       BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> round_error () { return 0.5L; }
3075       BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> infinity () { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::inf(); }
3076       BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> quiet_NaN () { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::nan(); }
3077       BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> signaling_NaN() { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); }
3078       BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> denorm_min () { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); }
3079    };
3080
3081 #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
3082
3083 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3084 BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::digits;
3085 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3086 BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::digits10;
3087 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3088 BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_digits10;
3089 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3090 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_signed;
3091 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3092 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_integer;
3093 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3094 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_exact;
3095 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3096 BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::radix;
3097 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3098 BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::min_exponent;
3099 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3100 BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::min_exponent10;
3101 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3102 BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_exponent;
3103 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3104 BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_exponent10;
3105 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3106 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_infinity;
3107 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3108 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_quiet_NaN;
3109 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3110 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_signaling_NaN;
3111 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3112 BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_denorm;
3113 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3114 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_denorm_loss;
3115 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3116 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_iec559;
3117 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3118 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_bounded;
3119 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3120 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_modulo;
3121 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3122 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::traps;
3123 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3124 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::tinyness_before;
3125 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3126 BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::round_style;
3127
3128 #endif
3129 }
3130
3131 namespace boost{ namespace math{
3132
3133 namespace policies{
3134
3135 template <unsigned Digits10, class ExponentType, class Allocator, class Policy, boost::multiprecision::expression_template_option ExpressionTemplates>
3136 struct precision< boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates>, Policy>
3137 {
3138    // Define a local copy of cpp_dec_float_digits10 because it might differ
3139    // from the template parameter Digits10 for small or large digit counts.
3140    static const boost::int32_t cpp_dec_float_digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10;
3141
3142    typedef typename Policy::precision_type precision_type;
3143    typedef digits2<((cpp_dec_float_digits10 + 1LL) * 1000LL) / 301LL> digits_2;
3144    typedef typename mpl::if_c<
3145       ((digits_2::value <= precision_type::value)
3146       || (Policy::precision_type::value <= 0)),
3147       // Default case, full precision for RealType:
3148       digits_2,
3149       // User customized precision:
3150       precision_type
3151    >::type type;
3152 };
3153
3154 } // namespace policies
3155
3156 }} // namespaces boost::math
3157
3158 #ifdef BOOST_MSVC
3159 #pragma warning(pop)
3160 #endif
3161
3162 #endif