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0001 ///////////////////////////////////////////////////////////////////////////////
0002 //  Copyright 2011 John Maddock.
0003 //  Copyright 2021 Matt Borland. Distributed under the Boost
0004 //  Software License, Version 1.0. (See accompanying file
0005 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
0006 
0007 #ifndef BOOST_MP_TOMMATH_HPP
0008 #define BOOST_MP_TOMMATH_HPP
0009 
0010 #include <cctype>
0011 #include <climits>
0012 #include <cmath>
0013 #include <cstdint>
0014 #include <cstddef>
0015 #include <cstdlib>
0016 #include <limits>
0017 #include <memory>
0018 #include <string>
0019 
0020 #include <tommath.h>
0021 
0022 #include <boost/multiprecision/detail/standalone_config.hpp>
0023 #include <boost/multiprecision/detail/fpclassify.hpp>
0024 #include <boost/multiprecision/number.hpp>
0025 #include <boost/multiprecision/rational_adaptor.hpp>
0026 #include <boost/multiprecision/detail/integer_ops.hpp>
0027 #include <boost/multiprecision/detail/hash.hpp>
0028 #include <boost/multiprecision/detail/no_exceptions_support.hpp>
0029 #include <boost/multiprecision/detail/assert.hpp>
0030 
0031 namespace boost {
0032 namespace multiprecision {
0033 namespace backends {
0034 
0035 namespace detail {
0036 
0037 template <class ErrType>
0038 inline void check_tommath_result(ErrType v)
0039 {
0040    if (v != MP_OKAY)
0041    {
0042       BOOST_MP_THROW_EXCEPTION(std::runtime_error(mp_error_to_string(v)));
0043    }
0044 }
0045 
0046 } // namespace detail
0047 
0048 void eval_multiply(tommath_int& t, const tommath_int& o);
0049 void eval_add(tommath_int& t, const tommath_int& o);
0050 
0051 struct tommath_int
0052 {
0053    using signed_types = std::tuple<std::int32_t, long long>  ;
0054    using unsigned_types = std::tuple<std::uint32_t, unsigned long long>;
0055    using float_types = std::tuple<long double>                            ;
0056 
0057    tommath_int()
0058    {
0059       detail::check_tommath_result(mp_init(&m_data));
0060    }
0061    tommath_int(const tommath_int& o)
0062    {
0063       detail::check_tommath_result(mp_init_copy(&m_data, const_cast< ::mp_int*>(&o.m_data)));
0064    }
0065    // rvalues:
0066    tommath_int(tommath_int&& o) noexcept
0067    {
0068       m_data      = o.m_data;
0069       o.m_data.dp = 0;
0070    }
0071    tommath_int& operator=(tommath_int&& o)
0072    {
0073       mp_exch(&m_data, &o.m_data);
0074       return *this;
0075    }
0076    tommath_int& operator=(const tommath_int& o)
0077    {
0078       if (m_data.dp == nullptr)
0079          detail::check_tommath_result(mp_init(&m_data));
0080       if (o.m_data.dp)
0081          detail::check_tommath_result(mp_copy(const_cast< ::mp_int*>(&o.m_data), &m_data));
0082       return *this;
0083    }
0084 #ifndef mp_get_u64
0085    // Pick off 32 bit chunks for mp_set_int:
0086    tommath_int& operator=(unsigned long long i)
0087    {
0088       if (m_data.dp == nullptr)
0089          detail::check_tommath_result(mp_init(&m_data));
0090       unsigned long long mask = ((1uLL << 32) - 1);
0091       unsigned shift = 0;
0092       ::mp_int t;
0093       detail::check_tommath_result(mp_init(&t));
0094       mp_zero(&m_data);
0095       while (i)
0096       {
0097          detail::check_tommath_result(mp_set_int(&t, static_cast<unsigned>(i & mask)));
0098          if (shift)
0099             detail::check_tommath_result(mp_mul_2d(&t, shift, &t));
0100          detail::check_tommath_result((mp_add(&m_data, &t, &m_data)));
0101          shift += 32;
0102          i >>= 32;
0103       }
0104       mp_clear(&t);
0105       return *this;
0106    }
0107 #elif !defined(ULLONG_MAX) || (ULLONG_MAX != 18446744073709551615uLL)
0108    // Pick off 64 bit chunks for mp_set_u64:
0109    tommath_int& operator=(unsigned long long i)
0110    {
0111       if (m_data.dp == nullptr)
0112          detail::check_tommath_result(mp_init(&m_data));
0113       if(sizeof(unsigned long long) * CHAR_BIT == 64)
0114       {
0115          mp_set_u64(&m_data, i);
0116          return *this;
0117       }
0118       unsigned long long mask = ((1uLL << 64) - 1);
0119       unsigned shift = 0;
0120       ::mp_int t;
0121       detail::check_tommath_result(mp_init(&t));
0122       mp_zero(&m_data);
0123       while (i)
0124       {
0125          detail::check_tommath_result(mp_set_u64(&t, static_cast<std::uint64_t>(i & mask)));
0126          if (shift)
0127             detail::check_tommath_result(mp_mul_2d(&t, shift, &t));
0128          detail::check_tommath_result((mp_add(&m_data, &t, &m_data)));
0129          shift += 64;
0130          i >>= 64;
0131       }
0132       mp_clear(&t);
0133       return *this;
0134    }
0135 #else
0136    tommath_int& operator=(unsigned long long i)
0137    {
0138       if (m_data.dp == nullptr)
0139          detail::check_tommath_result(mp_init(&m_data));
0140       mp_set_u64(&m_data, i);
0141       return *this;
0142    }
0143 #endif
0144    tommath_int& operator=(long long i)
0145    {
0146       if (m_data.dp == nullptr)
0147          detail::check_tommath_result(mp_init(&m_data));
0148       bool neg = i < 0;
0149       *this    = boost::multiprecision::detail::unsigned_abs(i);
0150       if (neg)
0151          detail::check_tommath_result(mp_neg(&m_data, &m_data));
0152       return *this;
0153    }
0154 #ifdef BOOST_HAS_INT128
0155    // Pick off 64 bit chunks for mp_set_u64:
0156    tommath_int& operator=(uint128_type i)
0157    {
0158       if (m_data.dp == nullptr)
0159          detail::check_tommath_result(mp_init(&m_data));
0160 
0161       int128_type  mask  = ((static_cast<uint128_type>(1u) << 64) - 1);
0162       unsigned           shift = 0;
0163       ::mp_int           t;
0164       detail::check_tommath_result(mp_init(&t));
0165       mp_zero(&m_data);
0166       while (i)
0167       {
0168 #ifndef mp_get_u32
0169          detail::check_tommath_result(mp_set_long_long(&t, static_cast<std::uint64_t>(i & mask)));
0170 #else
0171          mp_set_u64(&t, static_cast<std::uint64_t>(i & mask));
0172 #endif
0173          if (shift)
0174             detail::check_tommath_result(mp_mul_2d(&t, shift, &t));
0175          detail::check_tommath_result((mp_add(&m_data, &t, &m_data)));
0176          shift += 64;
0177          i >>= 64;
0178       }
0179       mp_clear(&t);
0180       return *this;
0181    }
0182    tommath_int& operator=(int128_type i)
0183    {
0184       if (m_data.dp == nullptr)
0185          detail::check_tommath_result(mp_init(&m_data));
0186       bool neg = i < 0;
0187       *this    = boost::multiprecision::detail::unsigned_abs(i);
0188       if (neg)
0189          detail::check_tommath_result(mp_neg(&m_data, &m_data));
0190       return *this;
0191    }
0192 #endif
0193    //
0194    // Note that although mp_set_int takes an unsigned long as an argument
0195    // it only sets the first 32-bits to the result, and ignores the rest.
0196    // So use uint32_t as the largest type to pass to this function.
0197    //
0198    tommath_int& operator=(std::uint32_t i)
0199    {
0200       if (m_data.dp == nullptr)
0201          detail::check_tommath_result(mp_init(&m_data));
0202 #ifndef mp_get_u32
0203       detail::check_tommath_result((mp_set_int(&m_data, i)));
0204 #else
0205       mp_set_u32(&m_data, i);
0206 #endif
0207       return *this;
0208    }
0209    tommath_int& operator=(std::int32_t i)
0210    {
0211       if (m_data.dp == nullptr)
0212          detail::check_tommath_result(mp_init(&m_data));
0213       bool neg = i < 0;
0214       *this    = boost::multiprecision::detail::unsigned_abs(i);
0215       if (neg)
0216          detail::check_tommath_result(mp_neg(&m_data, &m_data));
0217       return *this;
0218    }
0219    template <class F>
0220    tommath_int& assign_float(F a)
0221    {
0222       BOOST_MP_FLOAT128_USING using std::floor; using std::frexp; using std::ldexp;
0223 
0224       if (m_data.dp == nullptr)
0225          detail::check_tommath_result(mp_init(&m_data));
0226 
0227       if (a == 0)
0228       {
0229 #ifndef mp_get_u32
0230          detail::check_tommath_result(mp_set_int(&m_data, 0));
0231 #else
0232          mp_set_i32(&m_data, 0);
0233 #endif
0234          return *this;
0235       }
0236 
0237       if (a == 1)
0238       {
0239 #ifndef mp_get_u32
0240          detail::check_tommath_result(mp_set_int(&m_data, 1));
0241 #else
0242          mp_set_i32(&m_data, 1);
0243 #endif
0244          return *this;
0245       }
0246 
0247       BOOST_MP_ASSERT(!BOOST_MP_ISINF(a));
0248       BOOST_MP_ASSERT(!BOOST_MP_ISNAN(a));
0249 
0250       int         e;
0251       F f, term;
0252 #ifndef mp_get_u32
0253       detail::check_tommath_result(mp_set_int(&m_data, 0u));
0254 #else
0255       mp_set_i32(&m_data, 0);
0256 #endif
0257       ::mp_int t;
0258       detail::check_tommath_result(mp_init(&t));
0259 
0260       f = frexp(a, &e);
0261 
0262 #ifdef MP_DIGIT_BIT
0263       constexpr const int shift = std::numeric_limits<int>::digits - 1;
0264       using part_type = int     ;
0265 #else
0266       constexpr const int  shift = std::numeric_limits<std::int64_t>::digits - 1;
0267       using part_type = std::int64_t;
0268 #endif
0269 
0270       while (f)
0271       {
0272          // extract int sized bits from f:
0273          f    = ldexp(f, shift);
0274          term = floor(f);
0275          e -= shift;
0276          detail::check_tommath_result(mp_mul_2d(&m_data, shift, &m_data));
0277          if (term > 0)
0278          {
0279 #ifndef mp_get_u64
0280             detail::check_tommath_result(mp_set_int(&t, static_cast<part_type>(term)));
0281 #else
0282             mp_set_i64(&t, static_cast<part_type>(term));
0283 #endif
0284             detail::check_tommath_result(mp_add(&m_data, &t, &m_data));
0285          }
0286          else
0287          {
0288 #ifndef mp_get_u64
0289             detail::check_tommath_result(mp_set_int(&t, static_cast<part_type>(-term)));
0290 #else
0291             mp_set_i64(&t, static_cast<part_type>(-term));
0292 #endif
0293             detail::check_tommath_result(mp_sub(&m_data, &t, &m_data));
0294          }
0295          f -= term;
0296       }
0297       if (e > 0)
0298          detail::check_tommath_result(mp_mul_2d(&m_data, e, &m_data));
0299       else if (e < 0)
0300       {
0301          tommath_int t2;
0302          detail::check_tommath_result(mp_div_2d(&m_data, -e, &m_data, &t2.data()));
0303       }
0304       mp_clear(&t);
0305       return *this;
0306    }
0307    tommath_int& operator=(long double a)
0308    {
0309       return assign_float(a);
0310    }
0311 #ifdef BOOST_HAS_FLOAT128
0312    tommath_int& operator= (float128_type a)
0313    {
0314       return assign_float(a);
0315    }
0316 #endif
0317    tommath_int& operator=(const char* s)
0318    {
0319       //
0320       // We don't use libtommath's own routine because it doesn't error check the input :-(
0321       //
0322       if (m_data.dp == nullptr)
0323          detail::check_tommath_result(mp_init(&m_data));
0324       std::size_t n  = s ? std::strlen(s) : 0;
0325       *this          = static_cast<std::uint32_t>(0u);
0326       unsigned radix = 10;
0327       bool     isneg = false;
0328       if (n && (*s == '-'))
0329       {
0330          --n;
0331          ++s;
0332          isneg = true;
0333       }
0334       if (n && (*s == '0'))
0335       {
0336          if ((n > 1) && ((s[1] == 'x') || (s[1] == 'X')))
0337          {
0338             radix = 16;
0339             s += 2;
0340             n -= 2;
0341          }
0342          else
0343          {
0344             radix = 8;
0345             n -= 1;
0346          }
0347       }
0348       if (n)
0349       {
0350          if (radix == 8 || radix == 16)
0351          {
0352             unsigned shift = radix == 8 ? 3 : 4;
0353 #ifndef MP_DIGIT_BIT
0354             unsigned block_count = DIGIT_BIT / shift;
0355 #else
0356             unsigned block_count = MP_DIGIT_BIT / shift;
0357 #endif
0358             unsigned               block_shift = shift * block_count;
0359             unsigned long long val, block;
0360             while (*s)
0361             {
0362                block = 0;
0363                for (unsigned i = 0; (i < block_count); ++i)
0364                {
0365                   if (*s >= '0' && *s <= '9')
0366                      val = *s - '0';
0367                   else if (*s >= 'a' && *s <= 'f')
0368                      val = 10 + *s - 'a';
0369                   else if (*s >= 'A' && *s <= 'F')
0370                      val = 10 + *s - 'A';
0371                   else
0372                      val = 400;
0373                   if (val > radix)
0374                   {
0375                      BOOST_MP_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string."));
0376                   }
0377                   block <<= shift;
0378                   block |= val;
0379                   if (!*++s)
0380                   {
0381                      // final shift is different:
0382                      block_shift = (i + 1) * shift;
0383                      break;
0384                   }
0385                }
0386                detail::check_tommath_result(mp_mul_2d(&data(), block_shift, &data()));
0387                if (data().used)
0388                   data().dp[0] |= block;
0389                else
0390                   *this = block;
0391             }
0392          }
0393          else
0394          {
0395             // Base 10, we extract blocks of size 10^9 at a time, that way
0396             // the number of multiplications is kept to a minimum:
0397             std::uint32_t block_mult = 1000000000;
0398             while (*s)
0399             {
0400                std::uint32_t block = 0;
0401                for (unsigned i = 0; i < 9; ++i)
0402                {
0403                   std::uint32_t val;
0404                   if (*s >= '0' && *s <= '9')
0405                      val = *s - '0';
0406                   else
0407                      BOOST_MP_THROW_EXCEPTION(std::runtime_error("Unexpected character encountered in input."));
0408                   block *= 10;
0409                   block += val;
0410                   if (!*++s)
0411                   {
0412                      constexpr const std::uint32_t block_multiplier[9] = {10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000};
0413                      block_mult                                       = block_multiplier[i];
0414                      break;
0415                   }
0416                }
0417                tommath_int t;
0418                t = block_mult;
0419                eval_multiply(*this, t);
0420                t = block;
0421                eval_add(*this, t);
0422             }
0423          }
0424       }
0425       if (isneg)
0426          this->negate();
0427       return *this;
0428    }
0429    std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f) const
0430    {
0431       BOOST_MP_ASSERT(m_data.dp);
0432       int base = 10;
0433       if ((f & std::ios_base::oct) == std::ios_base::oct)
0434          base = 8;
0435       else if ((f & std::ios_base::hex) == std::ios_base::hex)
0436          base = 16;
0437       //
0438       // sanity check, bases 8 and 16 are only available for positive numbers:
0439       //
0440       if ((base != 10) && m_data.sign)
0441          BOOST_MP_THROW_EXCEPTION(std::runtime_error("Formatted output in bases 8 or 16 is only available for positive numbers"));
0442 
0443       int s;
0444       detail::check_tommath_result(mp_radix_size(const_cast< ::mp_int*>(&m_data), base, &s));
0445       std::unique_ptr<char[]> a(new char[s + 1]);
0446 #ifndef mp_to_binary
0447       detail::check_tommath_result(mp_toradix_n(const_cast< ::mp_int*>(&m_data), a.get(), base, s + 1));
0448 #else
0449       std::size_t written;
0450       detail::check_tommath_result(mp_to_radix(&m_data, a.get(), s + 1, &written, base));
0451 #endif
0452       std::string result = a.get();
0453       if (f & std::ios_base::uppercase)
0454          for (size_t i = 0; i < result.length(); ++i)
0455             result[i] = std::toupper(result[i]);
0456       if ((base != 10) && (f & std::ios_base::showbase))
0457       {
0458          int         pos = result[0] == '-' ? 1 : 0;
0459          const char* pp  = base == 8 ? "0" : (f & std::ios_base::uppercase) ? "0X" : "0x";
0460          result.insert(static_cast<std::string::size_type>(pos), pp);
0461       }
0462       if ((f & std::ios_base::showpos) && (result[0] != '-'))
0463          result.insert(static_cast<std::string::size_type>(0), 1, '+');
0464       if (((f & std::ios_base::uppercase) == 0) && (base == 16))
0465       {
0466          for (std::size_t i = 0; i < result.size(); ++i)
0467             result[i] = std::tolower(result[i]);
0468       }
0469       return result;
0470    }
0471    ~tommath_int()
0472    {
0473       if (m_data.dp)
0474          mp_clear(&m_data);
0475    }
0476    void negate()
0477    {
0478       BOOST_MP_ASSERT(m_data.dp);
0479       detail::check_tommath_result(mp_neg(&m_data, &m_data));
0480    }
0481    int compare(const tommath_int& o) const
0482    {
0483       BOOST_MP_ASSERT(m_data.dp && o.m_data.dp);
0484       return mp_cmp(const_cast< ::mp_int*>(&m_data), const_cast< ::mp_int*>(&o.m_data));
0485    }
0486    template <class V>
0487    int compare(V v) const
0488    {
0489       tommath_int d;
0490       tommath_int t(*this);
0491       detail::check_tommath_result(mp_shrink(&t.data()));
0492       d = v;
0493       return t.compare(d);
0494    }
0495    ::mp_int& data()
0496    {
0497       BOOST_MP_ASSERT(m_data.dp);
0498       return m_data;
0499    }
0500    const ::mp_int& data() const
0501    {
0502       BOOST_MP_ASSERT(m_data.dp);
0503       return m_data;
0504    }
0505    void swap(tommath_int& o) noexcept
0506    {
0507       mp_exch(&m_data, &o.data());
0508    }
0509 
0510  protected:
0511    ::mp_int m_data;
0512 };
0513 
0514 #ifndef mp_isneg
0515 #define BOOST_MP_TOMMATH_BIT_OP_CHECK(x) \
0516    if (SIGN(&x.data()))                  \
0517    BOOST_MP_THROW_EXCEPTION(std::runtime_error("Bitwise operations on libtommath negative valued integers are disabled as they produce unpredictable results"))
0518 #else
0519 #define BOOST_MP_TOMMATH_BIT_OP_CHECK(x) \
0520    if (mp_isneg(&x.data()))              \
0521    BOOST_MP_THROW_EXCEPTION(std::runtime_error("Bitwise operations on libtommath negative valued integers are disabled as they produce unpredictable results"))
0522 #endif
0523 
0524 int eval_get_sign(const tommath_int& val);
0525 
0526 inline void eval_add(tommath_int& t, const tommath_int& o)
0527 {
0528    detail::check_tommath_result(mp_add(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data()));
0529 }
0530 inline void eval_subtract(tommath_int& t, const tommath_int& o)
0531 {
0532    detail::check_tommath_result(mp_sub(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data()));
0533 }
0534 inline void eval_multiply(tommath_int& t, const tommath_int& o)
0535 {
0536    detail::check_tommath_result(mp_mul(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data()));
0537 }
0538 inline void eval_divide(tommath_int& t, const tommath_int& o)
0539 {
0540    using default_ops::eval_is_zero;
0541    tommath_int temp;
0542    if (eval_is_zero(o))
0543       BOOST_MP_THROW_EXCEPTION(std::overflow_error("Integer division by zero"));
0544    detail::check_tommath_result(mp_div(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data(), &temp.data()));
0545 }
0546 inline void eval_modulus(tommath_int& t, const tommath_int& o)
0547 {
0548    using default_ops::eval_is_zero;
0549    if (eval_is_zero(o))
0550       BOOST_MP_THROW_EXCEPTION(std::overflow_error("Integer division by zero"));
0551    bool neg  = eval_get_sign(t) < 0;
0552    bool neg2 = eval_get_sign(o) < 0;
0553    detail::check_tommath_result(mp_mod(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data()));
0554    if ((neg != neg2) && (eval_get_sign(t) != 0))
0555    {
0556       t.negate();
0557       detail::check_tommath_result(mp_add(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data()));
0558       t.negate();
0559    }
0560    else if (neg && (t.compare(o) == 0))
0561    {
0562       mp_zero(&t.data());
0563    }
0564 }
0565 template <class UI>
0566 inline void eval_left_shift(tommath_int& t, UI i)
0567 {
0568    detail::check_tommath_result(mp_mul_2d(&t.data(), static_cast<unsigned>(i), &t.data()));
0569 }
0570 template <class UI>
0571 inline void eval_right_shift(tommath_int& t, UI i)
0572 {
0573    using default_ops::eval_decrement;
0574    using default_ops::eval_increment;
0575    bool        neg = eval_get_sign(t) < 0;
0576    tommath_int d;
0577    if (neg)
0578       eval_increment(t);
0579    detail::check_tommath_result(mp_div_2d(&t.data(), static_cast<unsigned>(i), &t.data(), &d.data()));
0580    if (neg)
0581       eval_decrement(t);
0582 }
0583 template <class UI>
0584 inline void eval_left_shift(tommath_int& t, const tommath_int& v, UI i)
0585 {
0586    detail::check_tommath_result(mp_mul_2d(const_cast< ::mp_int*>(&v.data()), static_cast<unsigned>(i), &t.data()));
0587 }
0588 /*
0589 template <class UI>
0590 inline void eval_right_shift(tommath_int& t, const tommath_int& v, UI i)
0591 {
0592    tommath_int d;
0593    detail::check_tommath_result(mp_div_2d(const_cast< ::mp_int*>(&v.data()), static_cast<unsigned long>(i), &t.data(), &d.data()));
0594 }
0595 */
0596 inline void eval_bitwise_and(tommath_int& result, const tommath_int& v)
0597 {
0598    BOOST_MP_TOMMATH_BIT_OP_CHECK(result);
0599    BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
0600    detail::check_tommath_result(mp_and(&result.data(), const_cast< ::mp_int*>(&v.data()), &result.data()));
0601 }
0602 
0603 inline void eval_bitwise_or(tommath_int& result, const tommath_int& v)
0604 {
0605    BOOST_MP_TOMMATH_BIT_OP_CHECK(result);
0606    BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
0607    detail::check_tommath_result(mp_or(&result.data(), const_cast< ::mp_int*>(&v.data()), &result.data()));
0608 }
0609 
0610 inline void eval_bitwise_xor(tommath_int& result, const tommath_int& v)
0611 {
0612    BOOST_MP_TOMMATH_BIT_OP_CHECK(result);
0613    BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
0614    detail::check_tommath_result(mp_xor(&result.data(), const_cast< ::mp_int*>(&v.data()), &result.data()));
0615 }
0616 
0617 inline void eval_add(tommath_int& t, const tommath_int& p, const tommath_int& o)
0618 {
0619    detail::check_tommath_result(mp_add(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data()));
0620 }
0621 inline void eval_subtract(tommath_int& t, const tommath_int& p, const tommath_int& o)
0622 {
0623    detail::check_tommath_result(mp_sub(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data()));
0624 }
0625 inline void eval_multiply(tommath_int& t, const tommath_int& p, const tommath_int& o)
0626 {
0627    detail::check_tommath_result(mp_mul(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data()));
0628 }
0629 inline void eval_divide(tommath_int& t, const tommath_int& p, const tommath_int& o)
0630 {
0631    using default_ops::eval_is_zero;
0632    tommath_int d;
0633    if (eval_is_zero(o))
0634       BOOST_MP_THROW_EXCEPTION(std::overflow_error("Integer division by zero"));
0635    detail::check_tommath_result(mp_div(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data(), &d.data()));
0636 }
0637 inline void eval_modulus(tommath_int& t, const tommath_int& p, const tommath_int& o)
0638 {
0639    using default_ops::eval_is_zero;
0640    if (eval_is_zero(o))
0641       BOOST_MP_THROW_EXCEPTION(std::overflow_error("Integer division by zero"));
0642    bool neg  = eval_get_sign(p) < 0;
0643    bool neg2 = eval_get_sign(o) < 0;
0644    detail::check_tommath_result(mp_mod(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data()));
0645    if ((neg != neg2) && (eval_get_sign(t) != 0))
0646    {
0647       t.negate();
0648       detail::check_tommath_result(mp_add(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data()));
0649       t.negate();
0650    }
0651    else if (neg && (t.compare(o) == 0))
0652    {
0653       mp_zero(&t.data());
0654    }
0655 }
0656 
0657 inline void eval_bitwise_and(tommath_int& result, const tommath_int& u, const tommath_int& v)
0658 {
0659    BOOST_MP_TOMMATH_BIT_OP_CHECK(u);
0660    BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
0661    detail::check_tommath_result(mp_and(const_cast< ::mp_int*>(&u.data()), const_cast< ::mp_int*>(&v.data()), &result.data()));
0662 }
0663 
0664 inline void eval_bitwise_or(tommath_int& result, const tommath_int& u, const tommath_int& v)
0665 {
0666    BOOST_MP_TOMMATH_BIT_OP_CHECK(u);
0667    BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
0668    detail::check_tommath_result(mp_or(const_cast< ::mp_int*>(&u.data()), const_cast< ::mp_int*>(&v.data()), &result.data()));
0669 }
0670 
0671 inline void eval_bitwise_xor(tommath_int& result, const tommath_int& u, const tommath_int& v)
0672 {
0673    BOOST_MP_TOMMATH_BIT_OP_CHECK(u);
0674    BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
0675    detail::check_tommath_result(mp_xor(const_cast< ::mp_int*>(&u.data()), const_cast< ::mp_int*>(&v.data()), &result.data()));
0676 }
0677 /*
0678 inline void eval_complement(tommath_int& result, const tommath_int& u)
0679 {
0680    //
0681    // Although this code works, it doesn't really do what the user might expect....
0682    // and it's hard to see how it ever could.  Disabled for now:
0683    //
0684    result = u;
0685    for(int i = 0; i < result.data().used; ++i)
0686    {
0687       result.data().dp[i] = MP_MASK & ~(result.data().dp[i]);
0688    }
0689    //
0690    // We now need to pad out the left of the value with 1's to round up to a whole number of
0691    // CHAR_BIT * sizeof(mp_digit) units.  Otherwise we'll end up with a very strange number of
0692    // bits set!
0693    //
0694    unsigned shift = result.data().used * DIGIT_BIT;    // How many bits we're actually using
0695    // How many bits we actually need, reduced by one to account for a mythical sign bit:
0696    int padding = result.data().used * std::numeric_limits<mp_digit>::digits - shift - 1;
0697    while(padding >= std::numeric_limits<mp_digit>::digits)
0698       padding -= std::numeric_limits<mp_digit>::digits;
0699 
0700    // Create a mask providing the extra bits we need and add to result:
0701    tommath_int mask;
0702    mask = static_cast<long long>((1u << padding) - 1);
0703    eval_left_shift(mask, shift);
0704    add(result, mask);
0705 }
0706 */
0707 inline bool eval_is_zero(const tommath_int& val)
0708 {
0709    return mp_iszero(&val.data());
0710 }
0711 inline int eval_get_sign(const tommath_int& val)
0712 {
0713 #ifndef mp_isneg
0714    return mp_iszero(&val.data()) ? 0 : SIGN(&val.data()) ? -1 : 1;
0715 #else
0716    return mp_iszero(&val.data()) ? 0 : mp_isneg(&val.data()) ? -1 : 1;
0717 #endif
0718 }
0719 
0720 inline void eval_convert_to(unsigned long long* result, const tommath_int& val)
0721 {
0722    if (mp_isneg(&val.data()))
0723    {
0724       BOOST_MP_THROW_EXCEPTION(std::range_error("Converting negative arbitrary precision value to unsigned."));
0725    }
0726 #ifdef MP_DEPRECATED
0727    *result = mp_get_ull(&val.data());
0728 #else
0729    *result = mp_get_long_long(const_cast<mp_int*>(&val.data()));
0730 #endif
0731 }
0732 
0733 inline void eval_convert_to(long long* result, const tommath_int& val)
0734 {
0735    if (!mp_iszero(&val.data()) && (mp_count_bits(const_cast<::mp_int*>(&val.data())) > std::numeric_limits<long long>::digits))
0736    {
0737       *result = mp_isneg(&val.data()) ? (std::numeric_limits<long long>::min)() : (std::numeric_limits<long long>::max)();
0738       return;
0739    }
0740 #ifdef MP_DEPRECATED
0741    unsigned long long r = mp_get_mag_ull(&val.data());
0742 #else
0743    unsigned long long r = mp_get_long_long(const_cast<mp_int*>(&val.data()));
0744 #endif
0745    if (mp_isneg(&val.data()))
0746       *result = -static_cast<long long>(r);
0747    else
0748       *result = r;
0749 }
0750 
0751 #ifdef BOOST_HAS_INT128
0752 inline void eval_convert_to(uint128_type* result, const tommath_int& val)
0753 {
0754 #ifdef MP_DEPRECATED
0755    if (mp_ubin_size(&val.data()) > sizeof(uint128_type))
0756    {
0757       *result = ~static_cast<uint128_type>(0);
0758       return;
0759    }
0760    unsigned char buf[sizeof(uint128_type)];
0761    std::size_t   len;
0762    detail::check_tommath_result(mp_to_ubin(&val.data(), buf, sizeof(buf), &len));
0763    *result = 0;
0764    for (std::size_t i = 0; i < len; ++i)
0765    {
0766       *result <<= CHAR_BIT;
0767       *result |= buf[i];
0768    }
0769 #else
0770    std::size_t len = mp_unsigned_bin_size(const_cast<mp_int*>(&val.data()));
0771    if (len > sizeof(uint128_type))
0772    {
0773       *result = ~static_cast<uint128_type>(0);
0774       return;
0775    }
0776    unsigned char buf[sizeof(uint128_type)];
0777    detail::check_tommath_result(mp_to_unsigned_bin(const_cast<mp_int*>(&val.data()), buf));
0778    *result = 0;
0779    for (std::size_t i = 0; i < len; ++i)
0780    {
0781       *result <<= CHAR_BIT;
0782       *result |= buf[i];
0783    }
0784 #endif
0785 }
0786 inline void eval_convert_to(int128_type* result, const tommath_int& val)
0787 {
0788    uint128_type r;
0789    eval_convert_to(&r, val);
0790    if (mp_isneg(&val.data()))
0791       *result = -static_cast<int128_type>(r);
0792    else
0793       *result = r;
0794 }
0795 #endif
0796 #if defined(BOOST_HAS_FLOAT128)
0797 inline void eval_convert_to(float128_type* result, const tommath_int& val) noexcept
0798 {
0799    *result = float128_procs::strtoflt128(val.str(0, std::ios_base::scientific).c_str(), nullptr);
0800 }
0801 #endif
0802 inline void eval_convert_to(long double* result, const tommath_int& val) noexcept
0803 {
0804    *result = std::strtold(val.str(0, std::ios_base::scientific).c_str(), nullptr);
0805 }
0806 inline void eval_convert_to(double* result, const tommath_int& val) noexcept
0807 {
0808    *result = std::strtod(val.str(0, std::ios_base::scientific).c_str(), nullptr);
0809 }
0810 inline void eval_convert_to(float* result, const tommath_int& val) noexcept
0811 {
0812    *result = std::strtof(val.str(0, std::ios_base::scientific).c_str(), nullptr);
0813 }
0814 
0815 
0816 inline void eval_abs(tommath_int& result, const tommath_int& val)
0817 {
0818    detail::check_tommath_result(mp_abs(const_cast< ::mp_int*>(&val.data()), &result.data()));
0819 }
0820 inline void eval_gcd(tommath_int& result, const tommath_int& a, const tommath_int& b)
0821 {
0822    detail::check_tommath_result(mp_gcd(const_cast< ::mp_int*>(&a.data()), const_cast< ::mp_int*>(&b.data()), const_cast< ::mp_int*>(&result.data())));
0823 }
0824 inline void eval_lcm(tommath_int& result, const tommath_int& a, const tommath_int& b)
0825 {
0826    detail::check_tommath_result(mp_lcm(const_cast< ::mp_int*>(&a.data()), const_cast< ::mp_int*>(&b.data()), const_cast< ::mp_int*>(&result.data())));
0827 }
0828 inline void eval_powm(tommath_int& result, const tommath_int& base, const tommath_int& p, const tommath_int& m)
0829 {
0830    if (eval_get_sign(p) < 0)
0831    {
0832       BOOST_MP_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent."));
0833    }
0834    detail::check_tommath_result(mp_exptmod(const_cast< ::mp_int*>(&base.data()), const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&m.data()), &result.data()));
0835 }
0836 
0837 inline void eval_qr(const tommath_int& x, const tommath_int& y,
0838                     tommath_int& q, tommath_int& r)
0839 {
0840    detail::check_tommath_result(mp_div(const_cast< ::mp_int*>(&x.data()), const_cast< ::mp_int*>(&y.data()), &q.data(), &r.data()));
0841 }
0842 
0843 inline std::size_t eval_lsb(const tommath_int& val)
0844 {
0845    int c = eval_get_sign(val);
0846    if (c == 0)
0847    {
0848       BOOST_MP_THROW_EXCEPTION(std::domain_error("No bits were set in the operand."));
0849    }
0850    if (c < 0)
0851    {
0852       BOOST_MP_THROW_EXCEPTION(std::domain_error("Testing individual bits in negative values is not supported - results are undefined."));
0853    }
0854    return mp_cnt_lsb(const_cast< ::mp_int*>(&val.data()));
0855 }
0856 
0857 inline std::size_t eval_msb(const tommath_int& val)
0858 {
0859    int c = eval_get_sign(val);
0860    if (c == 0)
0861    {
0862       BOOST_MP_THROW_EXCEPTION(std::domain_error("No bits were set in the operand."));
0863    }
0864    if (c < 0)
0865    {
0866       BOOST_MP_THROW_EXCEPTION(std::domain_error("Testing individual bits in negative values is not supported - results are undefined."));
0867    }
0868    return mp_count_bits(const_cast< ::mp_int*>(&val.data())) - 1;
0869 }
0870 
0871 template <class Integer>
0872 inline typename std::enable_if<boost::multiprecision::detail::is_unsigned<Integer>::value, Integer>::type eval_integer_modulus(const tommath_int& x, Integer val)
0873 {
0874 #ifndef MP_DIGIT_BIT
0875    constexpr const mp_digit m = (static_cast<mp_digit>(1) << DIGIT_BIT) - 1;
0876 #else
0877    constexpr const mp_digit m = (static_cast<mp_digit>(1) << MP_DIGIT_BIT) - 1;
0878 #endif
0879    if (val <= m)
0880    {
0881       mp_digit d;
0882       detail::check_tommath_result(mp_mod_d(const_cast< ::mp_int*>(&x.data()), static_cast<mp_digit>(val), &d));
0883       return d;
0884    }
0885    else
0886    {
0887       return default_ops::eval_integer_modulus(x, val);
0888    }
0889 }
0890 template <class Integer>
0891 inline typename std::enable_if<boost::multiprecision::detail::is_signed<Integer>::value && boost::multiprecision::detail::is_integral<Integer>::value, Integer>::type eval_integer_modulus(const tommath_int& x, Integer val)
0892 {
0893    return eval_integer_modulus(x, boost::multiprecision::detail::unsigned_abs(val));
0894 }
0895 
0896 inline std::size_t hash_value(const tommath_int& val)
0897 {
0898    std::size_t result = 0;
0899    std::size_t len    = val.data().used;
0900    for (std::size_t i = 0; i < len; ++i)
0901       boost::multiprecision::detail::hash_combine(result, val.data().dp[i]);
0902    boost::multiprecision::detail::hash_combine(result, val.data().sign);
0903    return result;
0904 }
0905 
0906 } // namespace backends
0907 
0908 template <>
0909 struct number_category<tommath_int> : public std::integral_constant<int, number_kind_integer>
0910 {};
0911 
0912 }
0913 } // namespace boost::multiprecision
0914 
0915 namespace std {
0916 
0917 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0918 class numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >
0919 {
0920    using number_type = boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates>;
0921 
0922  public:
0923    static constexpr bool is_specialized = true;
0924    //
0925    // Largest and smallest numbers are bounded only by available memory, set
0926    // to zero:
0927    //
0928    static number_type(min)()
0929    {
0930       return number_type();
0931    }
0932    static number_type(max)()
0933    {
0934       return number_type();
0935    }
0936    static number_type                        lowest() { return (min)(); }
0937    static constexpr int                digits       = INT_MAX;
0938    static constexpr int                digits10     = (INT_MAX / 1000) * 301L;
0939    static constexpr int                max_digits10 = digits10 + 3;
0940    static constexpr bool               is_signed    = true;
0941    static constexpr bool               is_integer   = true;
0942    static constexpr bool               is_exact     = true;
0943    static constexpr int                radix        = 2;
0944    static number_type                        epsilon() { return number_type(); }
0945    static number_type                        round_error() { return number_type(); }
0946    static constexpr int                min_exponent      = 0;
0947    static constexpr int                min_exponent10    = 0;
0948    static constexpr int                max_exponent      = 0;
0949    static constexpr int                max_exponent10    = 0;
0950    static constexpr bool               has_infinity      = false;
0951    static constexpr bool               has_quiet_NaN     = false;
0952    static constexpr bool               has_signaling_NaN = false;
0953    static constexpr float_denorm_style has_denorm        = denorm_absent;
0954    static constexpr bool               has_denorm_loss   = false;
0955    static number_type                        infinity() { return number_type(); }
0956    static number_type                        quiet_NaN() { return number_type(); }
0957    static number_type                        signaling_NaN() { return number_type(); }
0958    static number_type                        denorm_min() { return number_type(); }
0959    static constexpr bool               is_iec559       = false;
0960    static constexpr bool               is_bounded      = false;
0961    static constexpr bool               is_modulo       = false;
0962    static constexpr bool               traps           = false;
0963    static constexpr bool               tinyness_before = false;
0964    static constexpr float_round_style  round_style     = round_toward_zero;
0965 };
0966 
0967 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0968 constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::digits;
0969 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0970 constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::digits10;
0971 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0972 constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::max_digits10;
0973 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0974 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_signed;
0975 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0976 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_integer;
0977 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0978 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_exact;
0979 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0980 constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::radix;
0981 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0982 constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::min_exponent;
0983 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0984 constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::min_exponent10;
0985 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0986 constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::max_exponent;
0987 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0988 constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::max_exponent10;
0989 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0990 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::has_infinity;
0991 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0992 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::has_quiet_NaN;
0993 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0994 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::has_signaling_NaN;
0995 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0996 constexpr float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::has_denorm;
0997 template <boost::multiprecision::expression_template_option ExpressionTemplates>
0998 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::has_denorm_loss;
0999 template <boost::multiprecision::expression_template_option ExpressionTemplates>
1000 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_iec559;
1001 template <boost::multiprecision::expression_template_option ExpressionTemplates>
1002 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_bounded;
1003 template <boost::multiprecision::expression_template_option ExpressionTemplates>
1004 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_modulo;
1005 template <boost::multiprecision::expression_template_option ExpressionTemplates>
1006 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::traps;
1007 template <boost::multiprecision::expression_template_option ExpressionTemplates>
1008 constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::tinyness_before;
1009 template <boost::multiprecision::expression_template_option ExpressionTemplates>
1010 constexpr float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::round_style;
1011 
1012 } // namespace std
1013 
1014 #endif
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