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boost/multiprecision/tommath.hpp

///////////////////////////////////////////////////////////////////////////////
//  Copyright 2011 John Maddock.
//  Copyright 2021 Matt Borland. Distributed under the Boost
//  Software License, Version 1.0. (See accompanying file
//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

#ifndef BOOST_MP_TOMMATH_HPP
#define BOOST_MP_TOMMATH_HPP

#include <cctype>
#include <climits>
#include <cmath>
#include <cstdint>
#include <cstddef>
#include <cstdlib>
#include <limits>
#include <memory>
#include <string>

#include <tommath.h>

#include <boost/multiprecision/detail/standalone_config.hpp>
#include <boost/multiprecision/detail/fpclassify.hpp>
#include <boost/multiprecision/number.hpp>
#include <boost/multiprecision/rational_adaptor.hpp>
#include <boost/multiprecision/detail/integer_ops.hpp>
#include <boost/multiprecision/detail/hash.hpp>
#include <boost/multiprecision/detail/no_exceptions_support.hpp>
#include <boost/multiprecision/detail/assert.hpp>

namespace boost {
namespace multiprecision {
namespace backends {

namespace detail {

template <class ErrType>
inline void check_tommath_result(ErrType v)
{
   if (v != MP_OKAY)
   {
      BOOST_MP_THROW_EXCEPTION(std::runtime_error(mp_error_to_string(v)));
   }
}

} // namespace detail

void eval_multiply(tommath_int& t, const tommath_int& o);
void eval_add(tommath_int& t, const tommath_int& o);

struct tommath_int
{
   using signed_types = std::tuple<std::int32_t, long long>  ;
   using unsigned_types = std::tuple<std::uint32_t, unsigned long long>;
   using float_types = std::tuple<long double>                            ;

   tommath_int()
   {
      detail::check_tommath_result(mp_init(&m_data));
   }
   tommath_int(const tommath_int& o)
   {
      detail::check_tommath_result(mp_init_copy(&m_data, const_cast< ::mp_int*>(&o.m_data)));
   }
   // rvalues:
   tommath_int(tommath_int&& o) noexcept
   {
      m_data      = o.m_data;
      o.m_data.dp = 0;
   }
   tommath_int& operator=(tommath_int&& o)
   {
      mp_exch(&m_data, &o.m_data);
      return *this;
   }
   tommath_int& operator=(const tommath_int& o)
   {
      if (m_data.dp == nullptr)
         detail::check_tommath_result(mp_init(&m_data));
      if (o.m_data.dp)
         detail::check_tommath_result(mp_copy(const_cast< ::mp_int*>(&o.m_data), &m_data));
      return *this;
   }
#ifndef mp_get_u64
   // Pick off 32 bit chunks for mp_set_int:
   tommath_int& operator=(unsigned long long i)
   {
      if (m_data.dp == nullptr)
         detail::check_tommath_result(mp_init(&m_data));
      unsigned long long mask = ((1uLL << 32) - 1);
      unsigned shift = 0;
      ::mp_int t;
      detail::check_tommath_result(mp_init(&t));
      mp_zero(&m_data);
      while (i)
      {
         detail::check_tommath_result(mp_set_int(&t, static_cast<unsigned>(i & mask)));
         if (shift)
            detail::check_tommath_result(mp_mul_2d(&t, shift, &t));
         detail::check_tommath_result((mp_add(&m_data, &t, &m_data)));
         shift += 32;
         i >>= 32;
      }
      mp_clear(&t);
      return *this;
   }
#elif !defined(ULLONG_MAX) || (ULLONG_MAX != 18446744073709551615uLL)
   // Pick off 64 bit chunks for mp_set_u64:
   tommath_int& operator=(unsigned long long i)
   {
      if (m_data.dp == nullptr)
         detail::check_tommath_result(mp_init(&m_data));
      if(sizeof(unsigned long long) * CHAR_BIT == 64)
      {
         mp_set_u64(&m_data, i);
         return *this;
      }
      unsigned long long mask = ((1uLL << 64) - 1);
      unsigned shift = 0;
      ::mp_int t;
      detail::check_tommath_result(mp_init(&t));
      mp_zero(&m_data);
      while (i)
      {
         detail::check_tommath_result(mp_set_u64(&t, static_cast<std::uint64_t>(i & mask)));
         if (shift)
            detail::check_tommath_result(mp_mul_2d(&t, shift, &t));
         detail::check_tommath_result((mp_add(&m_data, &t, &m_data)));
         shift += 64;
         i >>= 64;
      }
      mp_clear(&t);
      return *this;
   }
#else
   tommath_int& operator=(unsigned long long i)
   {
      if (m_data.dp == nullptr)
         detail::check_tommath_result(mp_init(&m_data));
      mp_set_u64(&m_data, i);
      return *this;
   }
#endif
   tommath_int& operator=(long long i)
   {
      if (m_data.dp == nullptr)
         detail::check_tommath_result(mp_init(&m_data));
      bool neg = i < 0;
      *this    = boost::multiprecision::detail::unsigned_abs(i);
      if (neg)
         detail::check_tommath_result(mp_neg(&m_data, &m_data));
      return *this;
   }
#ifdef BOOST_HAS_INT128
   // Pick off 64 bit chunks for mp_set_u64:
   tommath_int& operator=(uint128_type i)
   {
      if (m_data.dp == nullptr)
         detail::check_tommath_result(mp_init(&m_data));

      int128_type  mask  = ((static_cast<uint128_type>(1u) << 64) - 1);
      unsigned           shift = 0;
      ::mp_int           t;
      detail::check_tommath_result(mp_init(&t));
      mp_zero(&m_data);
      while (i)
      {
#ifndef mp_get_u32
         detail::check_tommath_result(mp_set_long_long(&t, static_cast<std::uint64_t>(i & mask)));
#else
         mp_set_u64(&t, static_cast<std::uint64_t>(i & mask));
#endif
         if (shift)
            detail::check_tommath_result(mp_mul_2d(&t, shift, &t));
         detail::check_tommath_result((mp_add(&m_data, &t, &m_data)));
         shift += 64;
         i >>= 64;
      }
      mp_clear(&t);
      return *this;
   }
   tommath_int& operator=(int128_type i)
   {
      if (m_data.dp == nullptr)
         detail::check_tommath_result(mp_init(&m_data));
      bool neg = i < 0;
      *this    = boost::multiprecision::detail::unsigned_abs(i);
      if (neg)
         detail::check_tommath_result(mp_neg(&m_data, &m_data));
      return *this;
   }
#endif
   //
   // Note that although mp_set_int takes an unsigned long as an argument
   // it only sets the first 32-bits to the result, and ignores the rest.
   // So use uint32_t as the largest type to pass to this function.
   //
   tommath_int& operator=(std::uint32_t i)
   {
      if (m_data.dp == nullptr)
         detail::check_tommath_result(mp_init(&m_data));
#ifndef mp_get_u32
      detail::check_tommath_result((mp_set_int(&m_data, i)));
#else
      mp_set_u32(&m_data, i);
#endif
      return *this;
   }
   tommath_int& operator=(std::int32_t i)
   {
      if (m_data.dp == nullptr)
         detail::check_tommath_result(mp_init(&m_data));
      bool neg = i < 0;
      *this    = boost::multiprecision::detail::unsigned_abs(i);
      if (neg)
         detail::check_tommath_result(mp_neg(&m_data, &m_data));
      return *this;
   }
   template <class F>
   tommath_int& assign_float(F a)
   {
      BOOST_MP_FLOAT128_USING using std::floor; using std::frexp; using std::ldexp;

      if (m_data.dp == nullptr)
         detail::check_tommath_result(mp_init(&m_data));

      if (a == 0)
      {
#ifndef mp_get_u32
         detail::check_tommath_result(mp_set_int(&m_data, 0));
#else
         mp_set_i32(&m_data, 0);
#endif
         return *this;
      }

      if (a == 1)
      {
#ifndef mp_get_u32
         detail::check_tommath_result(mp_set_int(&m_data, 1));
#else
         mp_set_i32(&m_data, 1);
#endif
         return *this;
      }

      BOOST_MP_ASSERT(!BOOST_MP_ISINF(a));
      BOOST_MP_ASSERT(!BOOST_MP_ISNAN(a));

      int         e;
      F f, term;
#ifndef mp_get_u32
      detail::check_tommath_result(mp_set_int(&m_data, 0u));
#else
      mp_set_i32(&m_data, 0);
#endif
      ::mp_int t;
      detail::check_tommath_result(mp_init(&t));

      f = frexp(a, &e);

#ifdef MP_DIGIT_BIT
      constexpr const int shift = std::numeric_limits<int>::digits - 1;
      using part_type = int     ;
#else
      constexpr const int  shift = std::numeric_limits<std::int64_t>::digits - 1;
      using part_type = std::int64_t;
#endif

      while (f)
      {
         // extract int sized bits from f:
         f    = ldexp(f, shift);
         term = floor(f);
         e -= shift;
         detail::check_tommath_result(mp_mul_2d(&m_data, shift, &m_data));
         if (term > 0)
         {
#ifndef mp_get_u64
            detail::check_tommath_result(mp_set_int(&t, static_cast<part_type>(term)));
#else
            mp_set_i64(&t, static_cast<part_type>(term));
#endif
            detail::check_tommath_result(mp_add(&m_data, &t, &m_data));
         }
         else
         {
#ifndef mp_get_u64
            detail::check_tommath_result(mp_set_int(&t, static_cast<part_type>(-term)));
#else
            mp_set_i64(&t, static_cast<part_type>(-term));
#endif
            detail::check_tommath_result(mp_sub(&m_data, &t, &m_data));
         }
         f -= term;
      }
      if (e > 0)
         detail::check_tommath_result(mp_mul_2d(&m_data, e, &m_data));
      else if (e < 0)
      {
         tommath_int t2;
         detail::check_tommath_result(mp_div_2d(&m_data, -e, &m_data, &t2.data()));
      }
      mp_clear(&t);
      return *this;
   }
   tommath_int& operator=(long double a)
   {
      return assign_float(a);
   }
#ifdef BOOST_HAS_FLOAT128
   tommath_int& operator= (float128_type a)
   {
      return assign_float(a);
   }
#endif
   tommath_int& operator=(const char* s)
   {
      //
      // We don't use libtommath's own routine because it doesn't error check the input :-(
      //
      if (m_data.dp == nullptr)
         detail::check_tommath_result(mp_init(&m_data));
      std::size_t n  = s ? std::strlen(s) : 0;
      *this          = static_cast<std::uint32_t>(0u);
      unsigned radix = 10;
      bool     isneg = false;
      if (n && (*s == '-'))
      {
         --n;
         ++s;
         isneg = true;
      }
      if (n && (*s == '0'))
      {
         if ((n > 1) && ((s[1] == 'x') || (s[1] == 'X')))
         {
            radix = 16;
            s += 2;
            n -= 2;
         }
         else
         {
            radix = 8;
            n -= 1;
         }
      }
      if (n)
      {
         if (radix == 8 || radix == 16)
         {
            unsigned shift = radix == 8 ? 3 : 4;
#ifndef MP_DIGIT_BIT
            unsigned block_count = DIGIT_BIT / shift;
#else
            unsigned block_count = MP_DIGIT_BIT / shift;
#endif
            unsigned               block_shift = shift * block_count;
            unsigned long long val, block;
            while (*s)
            {
               block = 0;
               for (unsigned i = 0; (i < block_count); ++i)
               {
                  if (*s >= '0' && *s <= '9')
                     val = *s - '0';
                  else if (*s >= 'a' && *s <= 'f')
                     val = 10 + *s - 'a';
                  else if (*s >= 'A' && *s <= 'F')
                     val = 10 + *s - 'A';
                  else
                     val = 400;
                  if (val > radix)
                  {
                     BOOST_MP_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string."));
                  }
                  block <<= shift;
                  block |= val;
                  if (!*++s)
                  {
                     // final shift is different:
                     block_shift = (i + 1) * shift;
                     break;
                  }
               }
               detail::check_tommath_result(mp_mul_2d(&data(), block_shift, &data()));
               if (data().used)
                  data().dp[0] |= block;
               else
                  *this = block;
            }
         }
         else
         {
            // Base 10, we extract blocks of size 10^9 at a time, that way
            // the number of multiplications is kept to a minimum:
            std::uint32_t block_mult = 1000000000;
            while (*s)
            {
               std::uint32_t block = 0;
               for (unsigned i = 0; i < 9; ++i)
               {
                  std::uint32_t val;
                  if (*s >= '0' && *s <= '9')
                     val = *s - '0';
                  else
                     BOOST_MP_THROW_EXCEPTION(std::runtime_error("Unexpected character encountered in input."));
                  block *= 10;
                  block += val;
                  if (!*++s)
                  {
                     constexpr const std::uint32_t block_multiplier[9] = {10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000};
                     block_mult                                       = block_multiplier[i];
                     break;
                  }
               }
               tommath_int t;
               t = block_mult;
               eval_multiply(*this, t);
               t = block;
               eval_add(*this, t);
            }
         }
      }
      if (isneg)
         this->negate();
      return *this;
   }
   std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f) const
   {
      BOOST_MP_ASSERT(m_data.dp);
      int base = 10;
      if ((f & std::ios_base::oct) == std::ios_base::oct)
         base = 8;
      else if ((f & std::ios_base::hex) == std::ios_base::hex)
         base = 16;
      //
      // sanity check, bases 8 and 16 are only available for positive numbers:
      //
      if ((base != 10) && m_data.sign)
         BOOST_MP_THROW_EXCEPTION(std::runtime_error("Formatted output in bases 8 or 16 is only available for positive numbers"));

      // Check against known removed macro that was removed around the same time as type was changed
      #ifdef mp_tobinary
      int s;
      #else
      size_t s;
      #endif
      detail::check_tommath_result(mp_radix_size(const_cast< ::mp_int*>(&m_data), base, &s));

      std::unique_ptr<char[]> a(new char[s + 1]);
#ifndef mp_to_binary
      detail::check_tommath_result(mp_toradix_n(const_cast< ::mp_int*>(&m_data), a.get(), base, s + 1));
#else
      std::size_t written;
      detail::check_tommath_result(mp_to_radix(&m_data, a.get(), s + 1, &written, base));
#endif
      std::string result = a.get();
      if (f & std::ios_base::uppercase)
         for (size_t i = 0; i < result.length(); ++i)
            result[i] = std::toupper(result[i]);
      if ((base != 10) && (f & std::ios_base::showbase))
      {
         int         pos = result[0] == '-' ? 1 : 0;
         const char* pp  = base == 8 ? "0" : (f & std::ios_base::uppercase) ? "0X" : "0x";
         result.insert(static_cast<std::string::size_type>(pos), pp);
      }
      if ((f & std::ios_base::showpos) && (result[0] != '-'))
         result.insert(static_cast<std::string::size_type>(0), 1, '+');
      if (((f & std::ios_base::uppercase) == 0) && (base == 16))
      {
         for (std::size_t i = 0; i < result.size(); ++i)
            result[i] = std::tolower(result[i]);
      }
      return result;
   }
   ~tommath_int()
   {
      if (m_data.dp)
         mp_clear(&m_data);
   }
   void negate()
   {
      BOOST_MP_ASSERT(m_data.dp);
      detail::check_tommath_result(mp_neg(&m_data, &m_data));
   }
   int compare(const tommath_int& o) const
   {
      BOOST_MP_ASSERT(m_data.dp && o.m_data.dp);
      return mp_cmp(const_cast< ::mp_int*>(&m_data), const_cast< ::mp_int*>(&o.m_data));
   }
   template <class V>
   int compare(V v) const
   {
      tommath_int d;
      tommath_int t(*this);
      detail::check_tommath_result(mp_shrink(&t.data()));
      d = v;
      return t.compare(d);
   }
   ::mp_int& data()
   {
      BOOST_MP_ASSERT(m_data.dp);
      return m_data;
   }
   const ::mp_int& data() const
   {
      BOOST_MP_ASSERT(m_data.dp);
      return m_data;
   }
   void swap(tommath_int& o) noexcept
   {
      mp_exch(&m_data, &o.data());
   }

 protected:
   ::mp_int m_data;
};

#ifndef mp_isneg
#define BOOST_MP_TOMMATH_BIT_OP_CHECK(x) \
   if (SIGN(&x.data()))                  \
   BOOST_MP_THROW_EXCEPTION(std::runtime_error("Bitwise operations on libtommath negative valued integers are disabled as they produce unpredictable results"))
#else
#define BOOST_MP_TOMMATH_BIT_OP_CHECK(x) \
   if (mp_isneg(&x.data()))              \
   BOOST_MP_THROW_EXCEPTION(std::runtime_error("Bitwise operations on libtommath negative valued integers are disabled as they produce unpredictable results"))
#endif

int eval_get_sign(const tommath_int& val);

inline void eval_add(tommath_int& t, const tommath_int& o)
{
   detail::check_tommath_result(mp_add(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data()));
}
inline void eval_subtract(tommath_int& t, const tommath_int& o)
{
   detail::check_tommath_result(mp_sub(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data()));
}
inline void eval_multiply(tommath_int& t, const tommath_int& o)
{
   detail::check_tommath_result(mp_mul(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data()));
}
inline void eval_divide(tommath_int& t, const tommath_int& o)
{
   using default_ops::eval_is_zero;
   tommath_int temp;
   if (eval_is_zero(o))
      BOOST_MP_THROW_EXCEPTION(std::overflow_error("Integer division by zero"));
   detail::check_tommath_result(mp_div(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data(), &temp.data()));
}
inline void eval_modulus(tommath_int& t, const tommath_int& o)
{
   using default_ops::eval_is_zero;
   if (eval_is_zero(o))
      BOOST_MP_THROW_EXCEPTION(std::overflow_error("Integer division by zero"));
   bool neg  = eval_get_sign(t) < 0;
   bool neg2 = eval_get_sign(o) < 0;
   detail::check_tommath_result(mp_mod(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data()));
   if ((neg != neg2) && (eval_get_sign(t) != 0))
   {
      t.negate();
      detail::check_tommath_result(mp_add(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data()));
      t.negate();
   }
   else if (neg && (t.compare(o) == 0))
   {
      mp_zero(&t.data());
   }
}
template <class UI>
inline void eval_left_shift(tommath_int& t, UI i)
{
   detail::check_tommath_result(mp_mul_2d(&t.data(), static_cast<unsigned>(i), &t.data()));
}
template <class UI>
inline void eval_right_shift(tommath_int& t, UI i)
{
   using default_ops::eval_decrement;
   using default_ops::eval_increment;
   bool        neg = eval_get_sign(t) < 0;
   tommath_int d;
   if (neg)
      eval_increment(t);
   detail::check_tommath_result(mp_div_2d(&t.data(), static_cast<unsigned>(i), &t.data(), &d.data()));
   if (neg)
      eval_decrement(t);
}
template <class UI>
inline void eval_left_shift(tommath_int& t, const tommath_int& v, UI i)
{
   detail::check_tommath_result(mp_mul_2d(const_cast< ::mp_int*>(&v.data()), static_cast<unsigned>(i), &t.data()));
}
/*
template <class UI>
inline void eval_right_shift(tommath_int& t, const tommath_int& v, UI i)
{
   tommath_int d;
   detail::check_tommath_result(mp_div_2d(const_cast< ::mp_int*>(&v.data()), static_cast<unsigned long>(i), &t.data(), &d.data()));
}
*/
inline void eval_bitwise_and(tommath_int& result, const tommath_int& v)
{
   BOOST_MP_TOMMATH_BIT_OP_CHECK(result);
   BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
   detail::check_tommath_result(mp_and(&result.data(), const_cast< ::mp_int*>(&v.data()), &result.data()));
}

inline void eval_bitwise_or(tommath_int& result, const tommath_int& v)
{
   BOOST_MP_TOMMATH_BIT_OP_CHECK(result);
   BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
   detail::check_tommath_result(mp_or(&result.data(), const_cast< ::mp_int*>(&v.data()), &result.data()));
}

inline void eval_bitwise_xor(tommath_int& result, const tommath_int& v)
{
   BOOST_MP_TOMMATH_BIT_OP_CHECK(result);
   BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
   detail::check_tommath_result(mp_xor(&result.data(), const_cast< ::mp_int*>(&v.data()), &result.data()));
}

inline void eval_add(tommath_int& t, const tommath_int& p, const tommath_int& o)
{
   detail::check_tommath_result(mp_add(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data()));
}
inline void eval_subtract(tommath_int& t, const tommath_int& p, const tommath_int& o)
{
   detail::check_tommath_result(mp_sub(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data()));
}
inline void eval_multiply(tommath_int& t, const tommath_int& p, const tommath_int& o)
{
   detail::check_tommath_result(mp_mul(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data()));
}
inline void eval_divide(tommath_int& t, const tommath_int& p, const tommath_int& o)
{
   using default_ops::eval_is_zero;
   tommath_int d;
   if (eval_is_zero(o))
      BOOST_MP_THROW_EXCEPTION(std::overflow_error("Integer division by zero"));
   detail::check_tommath_result(mp_div(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data(), &d.data()));
}
inline void eval_modulus(tommath_int& t, const tommath_int& p, const tommath_int& o)
{
   using default_ops::eval_is_zero;
   if (eval_is_zero(o))
      BOOST_MP_THROW_EXCEPTION(std::overflow_error("Integer division by zero"));
   bool neg  = eval_get_sign(p) < 0;
   bool neg2 = eval_get_sign(o) < 0;
   detail::check_tommath_result(mp_mod(const_cast< ::mp_int*>(&p.data()), const_cast< ::mp_int*>(&o.data()), &t.data()));
   if ((neg != neg2) && (eval_get_sign(t) != 0))
   {
      t.negate();
      detail::check_tommath_result(mp_add(&t.data(), const_cast< ::mp_int*>(&o.data()), &t.data()));
      t.negate();
   }
   else if (neg && (t.compare(o) == 0))
   {
      mp_zero(&t.data());
   }
}

inline void eval_bitwise_and(tommath_int& result, const tommath_int& u, const tommath_int& v)
{
   BOOST_MP_TOMMATH_BIT_OP_CHECK(u);
   BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
   detail::check_tommath_result(mp_and(const_cast< ::mp_int*>(&u.data()), const_cast< ::mp_int*>(&v.data()), &result.data()));
}

inline void eval_bitwise_or(tommath_int& result, const tommath_int& u, const tommath_int& v)
{
   BOOST_MP_TOMMATH_BIT_OP_CHECK(u);
   BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
   detail::check_tommath_result(mp_or(const_cast< ::mp_int*>(&u.data()), const_cast< ::mp_int*>(&v.data()), &result.data()));
}

inline void eval_bitwise_xor(tommath_int& result, const tommath_int& u, const tommath_int& v)
{
   BOOST_MP_TOMMATH_BIT_OP_CHECK(u);
   BOOST_MP_TOMMATH_BIT_OP_CHECK(v);
   detail::check_tommath_result(mp_xor(const_cast< ::mp_int*>(&u.data()), const_cast< ::mp_int*>(&v.data()), &result.data()));
}
/*
inline void eval_complement(tommath_int& result, const tommath_int& u)
{
   //
   // Although this code works, it doesn't really do what the user might expect....
   // and it's hard to see how it ever could.  Disabled for now:
   //
   result = u;
   for(int i = 0; i < result.data().used; ++i)
   {
      result.data().dp[i] = MP_MASK & ~(result.data().dp[i]);
   }
   //
   // We now need to pad out the left of the value with 1's to round up to a whole number of
   // CHAR_BIT * sizeof(mp_digit) units.  Otherwise we'll end up with a very strange number of
   // bits set!
   //
   unsigned shift = result.data().used * DIGIT_BIT;    // How many bits we're actually using
   // How many bits we actually need, reduced by one to account for a mythical sign bit:
   int padding = result.data().used * std::numeric_limits<mp_digit>::digits - shift - 1;
   while(padding >= std::numeric_limits<mp_digit>::digits)
      padding -= std::numeric_limits<mp_digit>::digits;

   // Create a mask providing the extra bits we need and add to result:
   tommath_int mask;
   mask = static_cast<long long>((1u << padding) - 1);
   eval_left_shift(mask, shift);
   add(result, mask);
}
*/
inline bool eval_is_zero(const tommath_int& val)
{
   return mp_iszero(&val.data());
}
inline int eval_get_sign(const tommath_int& val)
{
#ifndef mp_isneg
   return mp_iszero(&val.data()) ? 0 : SIGN(&val.data()) ? -1 : 1;
#else
   return mp_iszero(&val.data()) ? 0 : mp_isneg(&val.data()) ? -1 : 1;
#endif
}

inline void eval_convert_to(unsigned long long* result, const tommath_int& val)
{
   if (mp_isneg(&val.data()))
   {
      BOOST_MP_THROW_EXCEPTION(std::range_error("Converting negative arbitrary precision value to unsigned."));
   }
#ifdef MP_DEPRECATED
   *result = mp_get_ull(&val.data());
#else
   *result = mp_get_long_long(const_cast<mp_int*>(&val.data()));
#endif
}

inline void eval_convert_to(long long* result, const tommath_int& val)
{
   if (!mp_iszero(&val.data()) && (mp_count_bits(const_cast<::mp_int*>(&val.data())) > std::numeric_limits<long long>::digits))
   {
      *result = mp_isneg(&val.data()) ? (std::numeric_limits<long long>::min)() : (std::numeric_limits<long long>::max)();
      return;
   }
#ifdef MP_DEPRECATED
   unsigned long long r = mp_get_mag_ull(&val.data());
#else
   unsigned long long r = mp_get_long_long(const_cast<mp_int*>(&val.data()));
#endif
   if (mp_isneg(&val.data()))
      *result = -static_cast<long long>(r);
   else
      *result = r;
}

#ifdef BOOST_HAS_INT128
inline void eval_convert_to(uint128_type* result, const tommath_int& val)
{
#ifdef MP_DEPRECATED
   if (mp_ubin_size(&val.data()) > sizeof(uint128_type))
   {
      *result = ~static_cast<uint128_type>(0);
      return;
   }
   unsigned char buf[sizeof(uint128_type)];
   std::size_t   len;
   detail::check_tommath_result(mp_to_ubin(&val.data(), buf, sizeof(buf), &len));
   *result = 0;
   for (std::size_t i = 0; i < len; ++i)
   {
      *result <<= CHAR_BIT;
      *result |= buf[i];
   }
#else
   std::size_t len = mp_unsigned_bin_size(const_cast<mp_int*>(&val.data()));
   if (len > sizeof(uint128_type))
   {
      *result = ~static_cast<uint128_type>(0);
      return;
   }
   unsigned char buf[sizeof(uint128_type)];
   detail::check_tommath_result(mp_to_unsigned_bin(const_cast<mp_int*>(&val.data()), buf));
   *result = 0;
   for (std::size_t i = 0; i < len; ++i)
   {
      *result <<= CHAR_BIT;
      *result |= buf[i];
   }
#endif
}
inline void eval_convert_to(int128_type* result, const tommath_int& val)
{
   uint128_type r;
   eval_convert_to(&r, val);
   if (mp_isneg(&val.data()))
      *result = -static_cast<int128_type>(r);
   else
      *result = r;
}
#endif
#if defined(BOOST_HAS_FLOAT128)
inline void eval_convert_to(float128_type* result, const tommath_int& val) noexcept
{
   *result = float128_procs::strtoflt128(val.str(0, std::ios_base::scientific).c_str(), nullptr);
}
#endif
inline void eval_convert_to(long double* result, const tommath_int& val) noexcept
{
   *result = std::strtold(val.str(0, std::ios_base::scientific).c_str(), nullptr);
}
inline void eval_convert_to(double* result, const tommath_int& val) noexcept
{
   *result = std::strtod(val.str(0, std::ios_base::scientific).c_str(), nullptr);
}
inline void eval_convert_to(float* result, const tommath_int& val) noexcept
{
   *result = std::strtof(val.str(0, std::ios_base::scientific).c_str(), nullptr);
}


inline void eval_abs(tommath_int& result, const tommath_int& val)
{
   detail::check_tommath_result(mp_abs(const_cast< ::mp_int*>(&val.data()), &result.data()));
}
inline void eval_gcd(tommath_int& result, const tommath_int& a, const tommath_int& b)
{
   detail::check_tommath_result(mp_gcd(const_cast< ::mp_int*>(&a.data()), const_cast< ::mp_int*>(&b.data()), const_cast< ::mp_int*>(&result.data())));
}
inline void eval_lcm(tommath_int& result, const tommath_int& a, const tommath_int& b)
{
   detail::check_tommath_result(mp_lcm(const_cast< ::mp_int*>(&a.data()), const_cast< ::mp_int*>(&b.data()), const_cast< ::mp_int*>(&result.data())));
}
inline void eval_powm(tommath_int& result, const tommath_int& base, const tommath_int& p, const tommath_int& m)
{
   if (eval_get_sign(p) < 0)
   {
      BOOST_MP_THROW_EXCEPTION(std::runtime_error("powm requires a positive exponent."));
   }
   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()));
}

inline void eval_qr(const tommath_int& x, const tommath_int& y,
                    tommath_int& q, tommath_int& r)
{
   detail::check_tommath_result(mp_div(const_cast< ::mp_int*>(&x.data()), const_cast< ::mp_int*>(&y.data()), &q.data(), &r.data()));
}

inline std::size_t eval_lsb(const tommath_int& val)
{
   int c = eval_get_sign(val);
   if (c == 0)
   {
      BOOST_MP_THROW_EXCEPTION(std::domain_error("No bits were set in the operand."));
   }
   if (c < 0)
   {
      BOOST_MP_THROW_EXCEPTION(std::domain_error("Testing individual bits in negative values is not supported - results are undefined."));
   }
   return mp_cnt_lsb(const_cast< ::mp_int*>(&val.data()));
}

inline std::size_t eval_msb(const tommath_int& val)
{
   int c = eval_get_sign(val);
   if (c == 0)
   {
      BOOST_MP_THROW_EXCEPTION(std::domain_error("No bits were set in the operand."));
   }
   if (c < 0)
   {
      BOOST_MP_THROW_EXCEPTION(std::domain_error("Testing individual bits in negative values is not supported - results are undefined."));
   }
   return mp_count_bits(const_cast< ::mp_int*>(&val.data())) - 1;
}

template <class Integer>
inline typename std::enable_if<boost::multiprecision::detail::is_unsigned<Integer>::value, Integer>::type eval_integer_modulus(const tommath_int& x, Integer val)
{
#ifndef MP_DIGIT_BIT
   constexpr const mp_digit m = (static_cast<mp_digit>(1) << DIGIT_BIT) - 1;
#else
   constexpr const mp_digit m = (static_cast<mp_digit>(1) << MP_DIGIT_BIT) - 1;
#endif
   if (val <= m)
   {
      mp_digit d;
      detail::check_tommath_result(mp_mod_d(const_cast< ::mp_int*>(&x.data()), static_cast<mp_digit>(val), &d));
      return d;
   }
   else
   {
      return default_ops::eval_integer_modulus(x, val);
   }
}
template <class Integer>
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)
{
   return eval_integer_modulus(x, boost::multiprecision::detail::unsigned_abs(val));
}

inline std::size_t hash_value(const tommath_int& val)
{
   std::size_t result = 0;
   std::size_t len    = val.data().used;
   for (std::size_t i = 0; i < len; ++i)
      boost::multiprecision::detail::hash_combine(result, val.data().dp[i]);
   boost::multiprecision::detail::hash_combine(result, val.data().sign);
   return result;
}

} // namespace backends

template <>
struct number_category<tommath_int> : public std::integral_constant<int, number_kind_integer>
{};

}
} // namespace boost::multiprecision

namespace std {

template <boost::multiprecision::expression_template_option ExpressionTemplates>
class numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >
{
   using number_type = boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates>;

 public:
   static constexpr bool is_specialized = true;
   //
   // Largest and smallest numbers are bounded only by available memory, set
   // to zero:
   //
   static number_type(min)()
   {
      return number_type();
   }
   static number_type(max)()
   {
      return number_type();
   }
   static number_type                        lowest() { return (min)(); }
   static constexpr int                digits       = INT_MAX;
   static constexpr int                digits10     = (INT_MAX / 1000) * 301L;
   static constexpr int                max_digits10 = digits10 + 3;
   static constexpr bool               is_signed    = true;
   static constexpr bool               is_integer   = true;
   static constexpr bool               is_exact     = true;
   static constexpr int                radix        = 2;
   static number_type                        epsilon() { return number_type(); }
   static number_type                        round_error() { return number_type(); }
   static constexpr int                min_exponent      = 0;
   static constexpr int                min_exponent10    = 0;
   static constexpr int                max_exponent      = 0;
   static constexpr int                max_exponent10    = 0;
   static constexpr bool               has_infinity      = false;
   static constexpr bool               has_quiet_NaN     = false;
   static constexpr bool               has_signaling_NaN = false;
#ifdef _MSC_VER
#pragma warning(push)
#pragma warning(disable : 4996)
#endif
   static constexpr float_denorm_style       has_denorm      = denorm_absent;
#ifdef _MSC_VER
#pragma warning(pop)
#endif
   static constexpr bool                     has_denorm_loss = false;
   static number_type                        infinity() { return number_type(); }
   static number_type                        quiet_NaN() { return number_type(); }
   static number_type                        signaling_NaN() { return number_type(); }
   static number_type                        denorm_min() { return number_type(); }
   static constexpr bool               is_iec559       = false;
   static constexpr bool               is_bounded      = false;
   static constexpr bool               is_modulo       = false;
   static constexpr bool               traps           = false;
   static constexpr bool               tinyness_before = false;
   static constexpr float_round_style  round_style     = round_toward_zero;
};

template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::digits;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::digits10;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::max_digits10;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_signed;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_integer;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_exact;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::radix;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::min_exponent;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::min_exponent10;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::max_exponent;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::max_exponent10;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::has_infinity;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::has_quiet_NaN;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::has_signaling_NaN;
#ifdef _MSC_VER
#pragma warning(push)
#pragma warning(disable : 4996)
#endif
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::has_denorm;
#ifdef _MSC_VER
#pragma warning(pop)
#endif
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::has_denorm_loss;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_iec559;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_bounded;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_modulo;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::traps;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::tinyness_before;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::round_style;

} // namespace std

#endif