comparison DEPENDENCIES/generic/include/boost/multiprecision/tommath.hpp @ 16:2665513ce2d3

Add boost headers

+///////////////////////////////////////////////////////////////////////////////
+//  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 <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, long long>             signed_types;
+   typedef mpl::list<boost::uint32_t, unsigned long long>   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.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 = (unsigned long long i)
+   {
+      if(m_data.dp == 0)
+         detail::check_tommath_result(mp_init(&m_data));
+      unsigned long long 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 = (long long i)
+   {
+      BOOST_MP_USING_ABS
+      if(m_data.dp == 0)
+         detail::check_tommath_result(mp_init(&m_data));
+      bool neg = i < 0;
+      *this = static_cast<unsigned long long>(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 = static_cast<boost::uint32_t>(std::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;
+            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_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(pos, pp);
+      }
+      if((f & std::ios_base::showpos) && (result[0] != '-'))
+         result.insert(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)
+{
+   tommath_int d;
+   detail::check_tommath_result(mp_div_2d(&t.data(), static_cast<unsigned>(i), &t.data(), &d.data()));
+}
+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<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)
+{
+   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)
+{
+   typedef typename make_unsigned<Integer>::type unsigned_type;
+   return eval_integer_modulus(x, static_cast<unsigned_type>(std::abs(val)));
+}
+
+} // 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 + 2;
+   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