path: root/boost/multiprecision/tommath.hpp

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

#ifndef BOOST_MATH_MP_TOMMATH_BACKEND_HPP
#define BOOST_MATH_MP_TOMMATH_BACKEND_HPP

#include <boost/multiprecision/number.hpp>
#include <boost/multiprecision/rational_adaptor.hpp>
#include <boost/multiprecision/detail/integer_ops.hpp>
#include <boost/math/special_functions/fpclassify.hpp>
#include <boost/cstdint.hpp>
#include <boost/scoped_array.hpp>
#include <boost/functional/hash_fwd.hpp>
#include <tommath.h>
#include <cmath>
#include <limits>
#include <climits>

namespace boost{ namespace multiprecision{ namespace backends{

namespace detail{

inline void check_tommath_result(unsigned v)
{
   if(v != MP_OKAY)
   {
      BOOST_THROW_EXCEPTION(std::runtime_error(mp_error_to_string(v)));
   }
}

}

struct tommath_int;

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

struct tommath_int
{
   typedef mpl::list<boost::int32_t, boost::long_long_type>             signed_types;
   typedef mpl::list<boost::uint32_t, boost::ulong_long_type>   unsigned_types;
   typedef mpl::list<long double>                           float_types;

   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)));
   }
#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
   tommath_int(tommath_int&& o) BOOST_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;
   }
#endif
   tommath_int& operator = (const tommath_int& o)
   {
      if(m_data.dp == 0)
         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;
   }
   tommath_int& operator = (boost::ulong_long_type i)
   {
      if(m_data.dp == 0)
         detail::check_tommath_result(mp_init(&m_data));
      boost::ulong_long_type mask = ((1uLL << std::numeric_limits<unsigned>::digits) - 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 += std::numeric_limits<unsigned>::digits;
         i >>= std::numeric_limits<unsigned>::digits;
      }
      mp_clear(&t);
      return *this;
   }
   tommath_int& operator = (boost::long_long_type i)
   {
      if(m_data.dp == 0)
         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;
   }
   //
   // 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 = (boost::uint32_t i)
   {
      if(m_data.dp == 0)
         detail::check_tommath_result(mp_init(&m_data));
      detail::check_tommath_result((mp_set_int(&m_data, i)));
      return *this;
   }
   tommath_int& operator = (boost::int32_t i)
   {
      if(m_data.dp == 0)
         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;
   }
   tommath_int& operator = (long double a)
   {
      using std::frexp;
      using std::ldexp;
      using std::floor;

      if(m_data.dp == 0)
         detail::check_tommath_result(mp_init(&m_data));

      if (a == 0) {
         detail::check_tommath_result(mp_set_int(&m_data, 0));
         return *this;
      }

      if (a == 1) {
         detail::check_tommath_result(mp_set_int(&m_data, 1));
         return *this;
      }

      BOOST_ASSERT(!(boost::math::isinf)(a));
      BOOST_ASSERT(!(boost::math::isnan)(a));

      int e;
      long double f, term;
      detail::check_tommath_result(mp_set_int(&m_data, 0u));
      ::mp_int t;
      detail::check_tommath_result(mp_init(&t));

      f = frexp(a, &e);

      static const int shift = std::numeric_limits<int>::digits - 1;

      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)
         {
            detail::check_tommath_result(mp_set_int(&t, static_cast<int>(term)));
            detail::check_tommath_result(mp_add(&m_data, &t, &m_data));
         }
         else
         {
            detail::check_tommath_result(mp_set_int(&t, static_cast<int>(-term)));
            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 = (const char* s)
   {
      //
      // We don't use libtommath's own routine because it doesn't error check the input :-(
      //
      if(m_data.dp == 0)
         detail::check_tommath_result(mp_init(&m_data));
      std::size_t n = s ? std::strlen(s) : 0;
      *this = static_cast<boost::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;
            unsigned block_count = DIGIT_BIT / shift;
            unsigned block_shift = shift * block_count;
            boost::ulong_long_type 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_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:
            boost::uint32_t block_mult = 1000000000;
            while(*s)
            {
               boost::uint32_t block = 0;
               for(unsigned i = 0; i < 9; ++i)
               {
                  boost::uint32_t val;
                  if(*s >= '0' && *s <= '9')
                     val = *s - '0';
                  else
                     BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected character encountered in input."));
                  block *= 10;
                  block += val;
                  if(!*++s)
                  {
                     static const boost::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_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_THROW_EXCEPTION(std::runtime_error("Formatted output in bases 8 or 16 is only available for positive numbers"));
      int s;
      detail::check_tommath_result(mp_radix_size(const_cast< ::mp_int*>(&m_data), base, &s));
      boost::scoped_array<char> a(new char[s+1]);
      detail::check_tommath_result(mp_toradix_n(const_cast< ::mp_int*>(&m_data), a.get(), base, s+1));
      std::string result = a.get();
      if((base != 10) && (f & std::ios_base::showbase))
      {
         int pos = result[0] == '-' ? 1 : 0;
         const char* pp = base == 8 ? "0" : "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, '+');
      return result;
   }
   ~tommath_int()
   {
      if(m_data.dp)
         mp_clear(&m_data);
   }
   void negate()
   {
      BOOST_ASSERT(m_data.dp);
      mp_neg(&m_data, &m_data);
   }
   int compare(const tommath_int& o)const
   {
      BOOST_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_ASSERT(m_data.dp);
      return m_data; 
   }
   const ::mp_int& data()const 
   { 
      BOOST_ASSERT(m_data.dp);
      return m_data; 
   }
   void swap(tommath_int& o)BOOST_NOEXCEPT
   {
      mp_exch(&m_data, &o.data());
   }
protected:
   ::mp_int m_data;
};

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

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_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_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_increment;
   using default_ops::eval_decrement;
   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_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_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<boost::long_long_type>((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)
{
   return mp_iszero(&val.data()) ? 0 : SIGN(&val.data()) ? -1 : 1;
}
template <class A>
inline void eval_convert_to(A* result, const tommath_int& val)
{
   *result = boost::lexical_cast<A>(val.str(0, std::ios_base::fmtflags(0)));
}
inline void eval_convert_to(char* result, const tommath_int& val)
{
   *result = static_cast<char>(boost::lexical_cast<int>(val.str(0, std::ios_base::fmtflags(0))));
}
inline void eval_convert_to(unsigned char* result, const tommath_int& val)
{
   *result = static_cast<unsigned char>(boost::lexical_cast<unsigned>(val.str(0, std::ios_base::fmtflags(0))));
}
inline void eval_convert_to(signed char* result, const tommath_int& val)
{
   *result = static_cast<signed char>(boost::lexical_cast<int>(val.str(0, std::ios_base::fmtflags(0))));
}
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_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 unsigned eval_lsb(const tommath_int& val)
{
   int c = eval_get_sign(val);
   if(c == 0)
   {
      BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
   }
   if(c < 0)
   {
      BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
   }
   return mp_cnt_lsb(const_cast< ::mp_int*>(&val.data()));
}

inline unsigned eval_msb(const tommath_int& val)
{
   int c = eval_get_sign(val);
   if(c == 0)
   {
      BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
   }
   if(c < 0)
   {
      BOOST_THROW_EXCEPTION(std::range_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 enable_if<is_unsigned<Integer>, Integer>::type eval_integer_modulus(const tommath_int& x, Integer val)
{
   static const mp_digit m = (static_cast<mp_digit>(1) << DIGIT_BIT) - 1;
   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 enable_if<is_signed<Integer>, 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::hash_combine(result, val.data().dp[i]);
   boost::hash_combine(result, val.data().sign);
   return result;
}

} // namespace backends

using boost::multiprecision::backends::tommath_int;

template<>
struct number_category<tommath_int> : public mpl::int_<number_kind_integer>{};

typedef number<tommath_int >                     tom_int;
typedef rational_adaptor<tommath_int>               tommath_rational;
typedef number<tommath_rational>                 tom_rational;

}}  // namespaces

namespace std{

template<boost::multiprecision::expression_template_option ExpressionTemplates> 
class numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >
{
   typedef boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> number_type;
public:
   BOOST_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)(); }
   BOOST_STATIC_CONSTEXPR int digits = INT_MAX;
   BOOST_STATIC_CONSTEXPR int digits10 = (INT_MAX / 1000) * 301L;
   BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 3;
   BOOST_STATIC_CONSTEXPR bool is_signed = true;
   BOOST_STATIC_CONSTEXPR bool is_integer = true;
   BOOST_STATIC_CONSTEXPR bool is_exact = true;
   BOOST_STATIC_CONSTEXPR int radix = 2;
   static number_type epsilon() { return number_type(); }
   static number_type round_error() { return number_type(); }
   BOOST_STATIC_CONSTEXPR int min_exponent = 0;
   BOOST_STATIC_CONSTEXPR int min_exponent10 = 0;
   BOOST_STATIC_CONSTEXPR int max_exponent = 0;
   BOOST_STATIC_CONSTEXPR int max_exponent10 = 0;
   BOOST_STATIC_CONSTEXPR bool has_infinity = false;
   BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false;
   BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
   BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
   BOOST_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(); }
   BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
   BOOST_STATIC_CONSTEXPR bool is_bounded = false;
   BOOST_STATIC_CONSTEXPR bool is_modulo = false;
   BOOST_STATIC_CONSTEXPR bool traps = false;
   BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
   BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero;
};

#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION

template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::digits;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::digits10;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::max_digits10;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_signed;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_integer;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_exact;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::radix;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::min_exponent;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::min_exponent10;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::max_exponent;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::max_exponent10;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::has_infinity;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::has_quiet_NaN;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::has_signaling_NaN;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::has_denorm;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::has_denorm_loss;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_iec559;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_bounded;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::is_modulo;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::traps;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::tinyness_before;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::tommath_int, ExpressionTemplates> >::round_style;

#endif
}

#endif