/*
 ****************************************************************
 *          C++ Mathematical Expression Toolkit Library         *
 *                                                              *
 * Author: Arash Partow (1999-2012)                             *
 * URL: http://www.partow.net/programming/exprtk/index.html     *
 *                                                              *
 * Copyright notice:                                            *
 * Free use of the C++ Mathematical Expression Toolkit Library  *
 * is permitted under the guidelines and in accordance with the *
 * most current version of the Common Public License.           *
 * http://www.opensource.org/licenses/cpl1.0.php                *
 *                                                              *
 * Example expressions:                                         *
 * (00) (y+x/y)*(x-y/x)                                         *
 * (01) (x^2/sin(2*pi/y))-x/2                                   *
 * (02) sqrt(1-(x^2))                                           *
 * (03) 1-sin(2*x)+cos(pi/y)                                    *
 * (04) a*exp(2*t)+c                                            *
 * (05) if(((x+2)==3)and((y+5)<=9),1+w,2/z)                     *
 * (06) if(avg(x,y)<=x+y,x-y,x*y)+2*pi/x                        *
 * (07) z:=x+sin(2*pi/y)                                        *
 * (08) u:=2*(pi*z)/(w:=x+cos(y/pi))                            *
 * (09) clamp(-1,sin(2*pi*x)+cos(y/2*pi),+1)                    *
 * (10) inrange(-2,m,+2)==if(({-2<=m}and[m<=+2]),1,0)           *
 * (11) (12.34sin(x)cos(2y)7+1)==(12.34*sin(x)*cos(2*y)*7+1)    *
 * (12) (x ilike 's*ri?g') and [y<(3z^7+w)]                     *
 *                                                              *
 ****************************************************************
*/

#undef max
#undef min

#ifndef INCLUDE_EXPRTK_HPP
#define INCLUDE_EXPRTK_HPP

#include <cctype>
#include <iostream>
#include <string>
#include <algorithm>
#include <cmath>
#include <limits>
#include <deque>
#include <list>
#include <map>
#include <set>
#include <stack>


#define exprtk_lean_and_mean

#ifdef exprtk_lean_and_mean_numeric_only
   #ifndef exprtk_lean_and_mean
      #define exprtk_lean_and_mean
   #endif
   #ifndef exprtk_disable_string_capabilities
      #define exprtk_disable_string_capabilities
   #endif
#endif

#ifdef exprtk_lean_and_mean
   #ifndef exprtk_disable_extended_operator_optimizations
      #define exprtk_disable_extended_operator_optimizations
   #endif
   #ifndef exprtk_disable_extended_optimisations
      #define exprtk_disable_extended_optimisations
   #endif
#endif


namespace exprtk
{
   namespace details
   {
      inline bool is_whitespace(const char& c)
      {
         return (' '  == c) ||
                ('\n' == c) ||
                ('\r' == c) ||
                ('\t' == c) ||
                ('\b' == c);
      }

      inline bool is_operator_char(const char& c)
      {
         return ('+' == c) || ('-' == c) ||
                ('*' == c) || ('/' == c) ||
                ('^' == c) || ('<' == c) ||
                ('>' == c) || ('=' == c) ||
                (',' == c) || ('!' == c) ||
                ('(' == c) || (')' == c) ||
                ('[' == c) || (']' == c) ||
                ('{' == c) || ('}' == c) ||
                ('%' == c) || (':' == c) ||
                ('?' == c);
      }

      inline bool is_letter(const char c)
      {
         return (('a' <= c) && (c <= 'z')) || (('A' <= c) && (c <= 'Z'));
      }

      inline bool is_digit(const char c)
      {
         return ('0' <= c) && (c <= '9');
      }

      inline bool is_left_bracket(const char c)
      {
         return ('(' == c) || ('[' == c) || ('{' == c);
      }

      inline bool is_right_bracket(const char c)
      {
         return (')' == c) || (']' == c) || ('}' == c);
      }

      inline bool is_sign(const char c)
      {
         return ('+' == c) || ('-' == c);
      }

      inline bool is_invalid(const char& c)
      {
         return !is_whitespace(c)    &&
                !is_operator_char(c) &&
                !is_letter(c)        &&
                !is_digit(c)         &&
                ('.' != c)           &&
                ('_' != c)           &&
                ('$' != c)           &&
                ('\'' != c);
      }

      inline bool imatch(const char& c1, const char& c2)
      {
         return std::tolower(c1) == std::tolower(c2);
      }

      inline bool imatch(const std::string& s1, const std::string& s2)
      {
         if (s1.size() == s2.size())
         {
            for (std::size_t i = 0; i < s1.size(); ++i)
            {
               if (std::tolower(s1[i]) != std::tolower(s2[i]))
               {
                  return false;
               }
            }
            return true;
         }
         return false;
      }

      static const std::string reserved_words[] =
                                  {
                                     "and", "false", "for", "if", "ilike", "in", "like", "nand", "nor", "not",
                                     "or", "true", "while", "xor"
                                  };
      static const std::size_t reserved_words_size = sizeof(reserved_words) / sizeof(std::string);

      static const std::string reserved_symbols[] =
                                  {
                                     "abs", "acos", "and", "asin", "atan", "atan2", "avg", "ceil", "clamp",
                                     "cos", "cosh", "cot", "csc", "deg2grad", "deg2rad", "equal", "erf", "erfc",
                                     "exp", "false", "floor", "for", "grad2deg", "hyp", "if", "ilike", "in",
                                     "inrange", "like", "log", "log10", "logn", "max", "min", "mod", "mul",
                                     "nand", "nor", "not", "not_equal", "or", "rad2deg", "root", "round",
                                     "roundn", "sec", "sgn", "shl", "shr", "sin", "sinh", "sqrt", "sum",
                                     "tan", "tanh", "true", "while", "xor"
                                  };
      static const std::size_t reserved_symbols_size = sizeof(reserved_symbols) / sizeof(std::string);

      inline bool is_reserved_word(const std::string& symbol)
      {
         for (std::size_t i = 0; i < reserved_words_size; ++i)
         {
            if (imatch(symbol,reserved_words[i]))
            {
               return true;
            }
         }
         return false;
      }

      inline bool is_reserved_symbol(const std::string& symbol)
      {
         for (std::size_t i = 0; i < reserved_symbols_size; ++i)
         {
            if (imatch(symbol,reserved_symbols[i]))
            {
               return true;
            }
         }
         return false;
      }

      struct cs_match  { static inline bool cmp(const char c0, const char c1) { return c0 == c1; } };
      struct cis_match { static inline bool cmp(const char c0, const char c1) { return std::tolower(c0) == std::tolower(c1); } };

      template <typename Iterator, typename Compare>
      inline bool match_impl(const Iterator pattern_begin,
                             const Iterator pattern_end,
                             const Iterator data_begin,
                             const Iterator data_end,
                             const typename std::iterator_traits<Iterator>::value_type& zero_or_more,
                             const typename std::iterator_traits<Iterator>::value_type& zero_or_one)
      {
         if (0 == std::distance(data_begin,data_end)) return false;

         Iterator d_itr = data_begin;
         Iterator p_itr = pattern_begin;
         Iterator c_itr = data_begin;
         Iterator m_itr = data_begin;

         while ((data_end != d_itr) && (zero_or_more != (*p_itr)))
         {

            if ((!Compare::cmp((*p_itr),(*d_itr))) && (zero_or_one != (*p_itr)))
            {
               return false;
            }
            ++p_itr;
            ++d_itr;
         }

         while (data_end != d_itr)
         {
            if (zero_or_more == (*p_itr))
            {
               if (pattern_end == (++p_itr))
               {
                  return true;
               }
               m_itr = p_itr;
               c_itr = d_itr;
               ++c_itr;
            }
            else if ((Compare::cmp((*p_itr),(*d_itr))) || (zero_or_one == (*p_itr)))
            {
               ++p_itr;
               ++d_itr;
            }
            else
            {
               p_itr = m_itr;
               d_itr = c_itr++;
            }
         }

         while ((p_itr != pattern_end) && (zero_or_more == (*p_itr))) ++p_itr;

         return (p_itr == pattern_end);
      }

      inline bool wc_match(const std::string& wild_card,
                           const std::string& str)
      {
         return match_impl<const char*,cs_match>(wild_card.data(),
                                                 wild_card.data() + wild_card.size(),
                                                 str.data(),
                                                 str.data() + str.size(),
                                                 '*',
                                                 '?');
      }

      inline bool wc_imatch(const std::string& wild_card,
                            const std::string& str)
      {
         return match_impl<const char*,cis_match>(wild_card.data(),
                                                  wild_card.data() + wild_card.size(),
                                                  str.data(),
                                                  str.data() + str.size(),
                                                  '*',
                                                  '?');
      }

      static const double pow10[] = {
                                       1.0,
                                       10.0,
                                       100.0,
                                       1000.0,
                                       10000.0,
                                       100000.0,
                                       1000000.0,
                                       10000000.0,
                                       100000000.0,
                                       1000000000.0,
                                       10000000000.0,
                                       100000000000.0,
                                       1000000000000.0,
                                       10000000000000.0,
                                       100000000000000.0,
                                       1000000000000000.0,
                                       10000000000000000.0,
                                    };

      namespace numeric
      {
         namespace constant
         {
            static const double e       =  2.718281828459045235360;
            static const double pi      =  3.141592653589793238462;
            static const double pi_2    =  1.570796326794896619231;
            static const double pi_4    =  0.785398163397448309616;
            static const double pi_180  =  0.017453292519943295769;
            static const double _1_pi   =  0.318309886183790671538;
            static const double _2_pi   =  0.636619772367581343076;
            static const double _180_pi = 57.295779513082320876798;
         }

         namespace details
         {
            struct unknown_type_tag {};
            struct real_type_tag    {};
            struct int_type_tag     {};

            template <typename T>
            struct number_type { typedef unknown_type_tag type; };

            #define exprtk_register_real_type_tag(T)\
            template<> struct number_type<T> { typedef real_type_tag type; };

            #define exprtk_register_int_type_tag(T)\
            template<> struct number_type<T> { typedef int_type_tag type; };

            exprtk_register_real_type_tag(double)
            exprtk_register_real_type_tag(long double)
            exprtk_register_real_type_tag(float)
            exprtk_register_int_type_tag(short)
            exprtk_register_int_type_tag(int)
            exprtk_register_int_type_tag(long long int)
            exprtk_register_int_type_tag(unsigned short)
            exprtk_register_int_type_tag(unsigned int)
            exprtk_register_int_type_tag(unsigned long long int)

            #undef exprtk_register_real_type_tag
            #undef exprtk_register_int_type_tag

            template <typename T>
            inline T equal_impl(const T& v0, const T& v1, real_type_tag)
            {
               static const T epsilon = T(0.0000000001);
               return (std::abs(v0 - v1) <= (std::max(T(1),std::max(std::abs(v0),std::abs(v1))) * epsilon)) ? T(1) : T(0);
            }

            template <typename T>
            inline T equal_impl(const T& v0, const T& v1, int_type_tag)
            {
               return (v0 == v1) ? 1 : 0;
            }

            template <typename T>
            inline T nequal_impl(const T& v0, const T& v1, real_type_tag)
            {
               static const T epsilon = T(0.0000000001);
               return (std::abs(v0 - v1) > (std::max(T(1),std::max(std::abs(v0),std::abs(v1))) * epsilon)) ? T(1) : T(0);
            }

            template <typename T>
            inline T nequal_impl(const T& v0, const T& v1, int_type_tag)
            {
               return (v0 != v1) ? 1 : 0;
            }

            template <typename T>
            inline T modulus_impl(const T& v0, const T& v1, real_type_tag)
            {
               return std::fmod(v0,v1);
            }

            template <typename T>
            inline T modulus_impl(const T& v0, const T& v1, int_type_tag)
            {
               return v0 % v1;
            }

            template <typename T>
            inline T pow_impl(const T& v0, const T& v1, real_type_tag)
            {
               return std::pow(v0,v1);
            }

            template <typename T>
            inline T pow_impl(const T& v0, const T& v1, int_type_tag)
            {
               return std::pow(static_cast<double>(v0),static_cast<double>(v1));
            }

            template <typename T>
            inline T logn_impl(const T& v0, const T& v1, real_type_tag)
            {
               return std::log(v0) / std::log(v1);
            }

            template <typename T>
            inline T logn_impl(const T& v0, const T& v1, int_type_tag)
            {
               return static_cast<T>(logn_impl<double>(static_cast<double>(v0),static_cast<double>(v1),real_type_tag()));
            }

            template <typename T>
            inline T root_impl(const T& v0, const T& v1, real_type_tag)
            {
               return std::pow(v0,T(1)/v1);
            }

            template <typename T>
            inline T root_impl(const T& v0, const T& v1, int_type_tag)
            {
               return root_impl<double>(static_cast<double>(v0),static_cast<double>(v1),real_type_tag());
            }

            template <typename T>
            inline T roundn_impl(const T& v0, const T& v1, real_type_tag)
            {
               return T(std::floor((v0 * pow10[(int)std::floor(v1)]) + T(0.5)) / T(pow10[(int)std::floor(v1)]));
            }

            template <typename T>
            inline T roundn_impl(const T& v0, const T&, int_type_tag)
            {
               return v0;
            }

            template <typename T>
            inline T hyp_impl(const T& v0, const T& v1, real_type_tag)
            {
               return std::sqrt((v0 * v0) + (v1 * v1));
            }

            template <typename T>
            inline T hyp_impl(const T& v0, const T& v1, int_type_tag)
            {
               return static_cast<T>(std::sqrt(static_cast<double>((v0 * v0) + (v1 * v1))));
            }

            template <typename T>
            inline T atan2_impl(const T& v0, const T& v1, real_type_tag)
            {
               return std::atan2(v0,v1);
            }

            template <typename T>
            inline T atan2_impl(const T&, const T&, int_type_tag)
            {
               return 0;
            }

            template <typename T>
            inline T shr_impl(const T& v0, const T& v1, real_type_tag)
            {
               return v0 * (T(1) / std::pow(T(2),static_cast<T>(static_cast<int>(v1))));
            }

            template <typename T>
            inline T shr_impl(const T& v0, const T& v1, int_type_tag)
            {
               return v0 >> v1;
            }

            template <typename T>
            inline T shl_impl(const T& v0, const T& v1, real_type_tag)
            {
               return v0 * std::pow(T(2),static_cast<T>(static_cast<int>(v1)));
            }

            template <typename T>
            inline T shl_impl(const T& v0, const T& v1, int_type_tag)
            {
               return v0 << v1;
            }

            template <typename T>
            inline T sgn_impl(const T& v, real_type_tag)
            {
                    if (v > T(0.0)) return T(+1.0);
               else if (v < T(0.0)) return T(-1.0);
               else                 return T( 0.0);
            }

            template <typename T>
            inline T sgn_impl(const T& v, int_type_tag)
            {
                    if (v > T(0)) return T(+1);
               else if (v < T(0)) return T(-1);
               else               return T( 0);
            }

            template <typename T>
            inline T xor_impl(const T& v0, const T& v1, real_type_tag)
            {
               return v0 != v1;
            }

            template <typename T>
            inline T xor_impl(const T& v0, const T& v1, int_type_tag)
            {
               return v0 ^ v1;
            }

            template <typename T>
            inline T erf_impl(T v, real_type_tag)
            {
               #if defined(_WIN32) || defined(__WIN32__) || defined(WIN32)
               //Note: This should not be required for mscv 11.+
               T a1 =  T(+0.254829592);
               T a2 =  T(-0.284496736);
               T a3 =  T(+1.421413741);
               T a4 =  T(-1.453152027);
               T a5 =  T(+1.061405429);
               T p  =  T( 0.327591100);
               T sign = T(1.0);
               if (v < 0)
               {
                  sign = -1;
                  v = abs(v);
               }
               T t = T(1.0) / (T(1.0) + p * v);
               T y = T(1.0) - (((((a5 * t + a4) * t) + a3) * t + a2) * t + a1) * t * std::exp(-v * v);
               return sign * y;
               #else
               return ::erf(v);
               #endif
            }

            template <typename T>
            inline T erf_impl(T v, int_type_tag)
            {
               return erf_impl(static_cast<double>(v),real_type_tag());
            }

            template <typename T>
            inline T erfc_impl(T v, real_type_tag)
            {
               #if defined(_WIN32) || defined(__WIN32__) || defined(WIN32)
               return T(1.0) - erf_impl(v,real_type_tag());
               #else
               return ::erfc(v);
               #endif
            }

            template <typename T>
            inline T erfc_impl(T v, int_type_tag)
            {
               return erfc_impl(static_cast<double>(v),real_type_tag());
            }

            template <typename T> inline T   abs_impl(const T& v, real_type_tag) { return std::abs  (v); }
            template <typename T> inline T  acos_impl(const T& v, real_type_tag) { return std::acos (v); }
            template <typename T> inline T  asin_impl(const T& v, real_type_tag) { return std::asin (v); }
            template <typename T> inline T  atan_impl(const T& v, real_type_tag) { return std::atan (v); }
            template <typename T> inline T  ceil_impl(const T& v, real_type_tag) { return std::ceil (v); }
            template <typename T> inline T   cos_impl(const T& v, real_type_tag) { return std::cos  (v); }
            template <typename T> inline T  cosh_impl(const T& v, real_type_tag) { return std::cosh (v); }
            template <typename T> inline T   exp_impl(const T& v, real_type_tag) { return std::exp  (v); }
            template <typename T> inline T floor_impl(const T& v, real_type_tag) { return std::floor(v); }
            template <typename T> inline T   log_impl(const T& v, real_type_tag) { return std::log  (v); }
            template <typename T> inline T log10_impl(const T& v, real_type_tag) { return std::log10(v); }
            template <typename T> inline T   neg_impl(const T& v, real_type_tag) { return -v;            }
            template <typename T> inline T   pos_impl(const T& v, real_type_tag) { return +v;            }
            template <typename T> inline T round_impl(const T& v, real_type_tag) { return std::floor(v + T(0.5)); }
            template <typename T> inline T   sin_impl(const T& v, real_type_tag) { return std::sin  (v); }
            template <typename T> inline T  sinh_impl(const T& v, real_type_tag) { return std::sinh (v); }
            template <typename T> inline T  sqrt_impl(const T& v, real_type_tag) { return std::sqrt (v); }
            template <typename T> inline T   tan_impl(const T& v, real_type_tag) { return std::tan  (v); }
            template <typename T> inline T  tanh_impl(const T& v, real_type_tag) { return std::tanh (v); }
            template <typename T> inline T   cot_impl(const T& v, real_type_tag) { return T(1) / std::tan(v); }
            template <typename T> inline T   sec_impl(const T& v, real_type_tag) { return T(1) / std::cos(v); }
            template <typename T> inline T   csc_impl(const T& v, real_type_tag) { return T(1) / std::sin(v); }
            template <typename T> inline T   r2d_impl(const T& v, real_type_tag) { return (v * T(numeric::constant::_180_pi)); }
            template <typename T> inline T   d2r_impl(const T& v, real_type_tag) { return (v * T(numeric::constant::pi_180));  }
            template <typename T> inline T   d2g_impl(const T& v, real_type_tag) { return (v * T(20.0/9.0)); }
            template <typename T> inline T   g2d_impl(const T& v, real_type_tag) { return (v * T(9.0/20.0)); }
            template <typename T> inline T  notl_impl(const T& v, real_type_tag) { return (v != T(0) ? T(0) : T(1)); }

            template <typename T> inline T   abs_impl(const T& v, int_type_tag) { return std::abs  (v); }
            template <typename T> inline T   exp_impl(const T& v, int_type_tag) { return std::exp  (v); }
            template <typename T> inline T   log_impl(const T& v, int_type_tag) { return std::log  (v); }
            template <typename T> inline T log10_impl(const T& v, int_type_tag) { return std::log10(v); }
            template <typename T> inline T   neg_impl(const T& v, int_type_tag) { return -v;            }
            template <typename T> inline T   pos_impl(const T& v, int_type_tag) { return +v;            }
            template <typename T> inline T  ceil_impl(const T& v, int_type_tag) { return v;             }
            template <typename T> inline T floor_impl(const T& v, int_type_tag) { return v;             }
            template <typename T> inline T round_impl(const T& v, int_type_tag) { return v;             }
            template <typename T> inline T  notl_impl(const T& v, int_type_tag) { return !v;            }
            template <typename T> inline T  sqrt_impl(const T& v, int_type_tag) { return std::sqrt (v); }
            template <typename T> inline T  acos_impl(const T&  , int_type_tag) { return std::numeric_limits<T>::quiet_NaN(); }
            template <typename T> inline T  asin_impl(const T&  , int_type_tag) { return std::numeric_limits<T>::quiet_NaN(); }
            template <typename T> inline T  atan_impl(const T&  , int_type_tag) { return std::numeric_limits<T>::quiet_NaN(); }
            template <typename T> inline T   cos_impl(const T&  , int_type_tag) { return std::numeric_limits<T>::quiet_NaN(); }
            template <typename T> inline T  cosh_impl(const T&  , int_type_tag) { return std::numeric_limits<T>::quiet_NaN(); }
            template <typename T> inline T   sin_impl(const T&  , int_type_tag) { return std::numeric_limits<T>::quiet_NaN(); }
            template <typename T> inline T  sinh_impl(const T&  , int_type_tag) { return std::numeric_limits<T>::quiet_NaN(); }
            template <typename T> inline T   tan_impl(const T&  , int_type_tag) { return std::numeric_limits<T>::quiet_NaN(); }
            template <typename T> inline T  tanh_impl(const T&  , int_type_tag) { return std::numeric_limits<T>::quiet_NaN(); }
            template <typename T> inline T   cot_impl(const T&  , int_type_tag) { return std::numeric_limits<T>::quiet_NaN(); }
            template <typename T> inline T   sec_impl(const T&  , int_type_tag) { return std::numeric_limits<T>::quiet_NaN(); }
            template <typename T> inline T   csc_impl(const T&  , int_type_tag) { return std::numeric_limits<T>::quiet_NaN(); }

            template <typename T>
            inline bool is_integer_impl(const T& v, real_type_tag)
            {
               return (T(0.0) == std::fmod(v,T(1.0)));
            }

            template <typename T>
            inline bool is_integer_impl(const T&, int_type_tag)
            {
               return true;
            }

         }

         template <typename Type>
         struct numeric_info { enum { length = 0, size = 32, bound_length = 0, min_exp = 0, max_exp = 0 }; };

         template<> struct numeric_info<int>         { enum { length = 10, size = 16, bound_length =  9}; };
         template<> struct numeric_info<float>       { enum { min_exp =  -38, max_exp =  +38}; };
         template<> struct numeric_info<double>      { enum { min_exp = -308, max_exp = +308}; };
         template<> struct numeric_info<long double> { enum { min_exp = -308, max_exp = +308}; };

         template <typename T>
         inline T equal(const T& v0, const T& v1)
         {
            typename details::number_type<T>::type num_type;
            return details::equal_impl(v0,v1,num_type);
         }

         template <typename T>
         inline T nequal(const T& v0, const T& v1)
         {
            typename details::number_type<T>::type num_type;
            return details::nequal_impl(v0,v1,num_type);
         }

         template <typename T>
         inline T modulus(const T& v0, const T& v1)
         {
            typename details::number_type<T>::type num_type;
            return details::modulus_impl(v0,v1,num_type);
         }

         template <typename T>
         inline T pow(const T& v0, const T& v1)
         {
            typename details::number_type<T>::type num_type;
            return details::pow_impl(v0,v1,num_type);
         }

         template <typename T>
         inline T logn(const T& v0, const T& v1)
         {
            typename details::number_type<T>::type num_type;
            return details::logn_impl(v0,v1,num_type);
         }

         template <typename T>
         inline T root(const T& v0, const T& v1)
         {
            typename details::number_type<T>::type num_type;
            return details::root_impl(v0,v1,num_type);
         }

         template <typename T>
         inline T roundn(const T& v0, const T& v1)
         {
            typename details::number_type<T>::type num_type;
            return details::roundn_impl(v0,v1,num_type);
         }

         template <typename T>
         inline T hyp(const T& v0, const T& v1)
         {
            typename details::number_type<T>::type num_type;
            return details::hyp_impl(v0,v1,num_type);
         }

         template <typename T>
         inline T atan2(const T& v0, const T& v1)
         {
            typename details::number_type<T>::type num_type;
            return details::atan2_impl(v0,v1,num_type);
         }

         template <typename T>
         inline T shr(const T& v0, const T& v1)
         {
            typename details::number_type<T>::type num_type;
            return details::shr_impl(v0,v1,num_type);
         }

         template <typename T>
         inline T shl(const T& v0, const T& v1)
         {
            typename details::number_type<T>::type num_type;
            return details::shl_impl(v0,v1,num_type);
         }

         template <typename T>
         inline T xor_opr(const T& v0, const T& v1)
         {
            typename details::number_type<T>::type num_type;
            return details::xor_impl(v0,v1,num_type);
         }

         template <typename T>
         inline bool is_integer(const T& v)
         {
            typename details::number_type<T>::type num_type;
            return details::is_integer_impl(v,num_type);
         }

         template <typename T, unsigned int N>
         struct fast_exp
         {
            static inline T result(T v)
            {
               unsigned int k = N;
               T l = T(1);
               while (k)
               {
                  if (k & 1)
                  {
                     l *= v;
                     --k;
                  }
                  v *= v;
                  k >>= 1;
               }
               return l;
            }
         };

         template <typename T> struct fast_exp<T,10> { static inline T result(T v) { T v_5 = fast_exp<T,5>::result(v); return v_5 * v_5; } };
         template <typename T> struct fast_exp<T, 9> { static inline T result(T v) { return fast_exp<T,8>::result(v) * v; } };
         template <typename T> struct fast_exp<T, 8> { static inline T result(T v) { T v_4 = fast_exp<T,4>::result(v); return v_4 * v_4; } };
         template <typename T> struct fast_exp<T, 7> { static inline T result(T v) { return fast_exp<T,6>::result(v) * v; } };
         template <typename T> struct fast_exp<T, 6> { static inline T result(T v) { T v_3 = fast_exp<T,3>::result(v); return v_3 * v_3; } };
         template <typename T> struct fast_exp<T, 5> { static inline T result(T v) { return fast_exp<T,4>::result(v) * v; } };
         template <typename T> struct fast_exp<T, 4> { static inline T result(T v) { T v_2 = v * v; return v_2 * v_2; } };
         template <typename T> struct fast_exp<T, 3> { static inline T result(T v) { return v * v * v; } };
         template <typename T> struct fast_exp<T, 2> { static inline T result(T v) { return v * v;     } };
         template <typename T> struct fast_exp<T, 1> { static inline T result(T v) { return v;         } };
         template <typename T> struct fast_exp<T, 0> { static inline T result(T  ) { return T(1);      } };

         #define exprtk_define_unary_function(FunctionName) \
         template <typename T> \
         inline T FunctionName (const T& v) \
         { \
            typename details::number_type<T>::type num_type; \
            return details:: FunctionName##_impl(v,num_type); \
         }

         exprtk_define_unary_function(abs  )
         exprtk_define_unary_function(acos )
         exprtk_define_unary_function(asin )
         exprtk_define_unary_function(atan )
         exprtk_define_unary_function(ceil )
         exprtk_define_unary_function(cos  )
         exprtk_define_unary_function(cosh )
         exprtk_define_unary_function(exp  )
         exprtk_define_unary_function(floor)
         exprtk_define_unary_function(log  )
         exprtk_define_unary_function(log10)
         exprtk_define_unary_function(neg  )
         exprtk_define_unary_function(pos  )
         exprtk_define_unary_function(round)
         exprtk_define_unary_function(sin  )
         exprtk_define_unary_function(sinh )
         exprtk_define_unary_function(sqrt )
         exprtk_define_unary_function(tan  )
         exprtk_define_unary_function(tanh )
         exprtk_define_unary_function(cot  )
         exprtk_define_unary_function(sec  )
         exprtk_define_unary_function(csc  )
         exprtk_define_unary_function(r2d  )
         exprtk_define_unary_function(d2r  )
         exprtk_define_unary_function(d2g  )
         exprtk_define_unary_function(g2d  )
         exprtk_define_unary_function(notl )
         exprtk_define_unary_function(sgn  )
         exprtk_define_unary_function(erf  )
         exprtk_define_unary_function(erfc )
         #undef exprtk_define_unary_function
      }

      template <typename T>
      struct token
      {

         enum token_type
         {
            none        =   0,
            error       =   1,
            eof         =   2,
            number      =   3,
            symbol      =   4,
            string      =   5,
            assign      =   6,
            shr         =   7,
            shl         =   8,
            lte         =   9,
            ne          =  10,
            gte         =  11,
            lt          = '<',
            gt          = '>',
            eq          = '=',
            rbracket    = ')',
            lbracket    = '(',
            rsqrbracket = ']',
            lsqrbracket = '[',
            rcrlbracket = '}',
            lcrlbracket = '{',
            comma       = ',',
            add         = '+',
            sub         = '-',
            div         = '/',
            mul         = '*',
            mod         = '%',
            pow         = '^'
         };

         token() {}

         explicit token(token_type ttype)
         : type(ttype)
         {}

         token(token_type ttype,
               const char* begin, const char* end)
         : type(ttype),
           value(std::string(begin,end)),
           numeric_value(T(0))
         {}

         token(token_type ttype, const std::string& v)
         : type(ttype),
           value(v),
           numeric_value(T(0))
         {}

         token(token_type ttype, const T& num_val)
         : type(ttype),
           numeric_value(num_val)
         {}

         token_type type;
         std::string value;
         T numeric_value;
      };

      template <typename T>
      class lexer
      {
      public:

         typedef token<T> token_t;

         inline bool process(const std::string& str)
         {
            error_description_ = "";
            s_itr = str.data();
            s_end = str.data() + str.size();
            eof_token_ = token_t(token_t::eof,s_end,s_end);
            token_list_.clear();
            while (s_end != s_itr)
            {
               scan_token();
               if (!error_description_.empty())
               {
                  return false;
               }
            }
            process_commutative_symbols();
            token_itr_ = token_list_.begin();
            store_token_itr_ = token_list_.begin();
            return true;
         }

         inline void store()
         {
            store_token_itr_ = token_itr_;
         }

         inline void restore()
         {
            token_itr_ = store_token_itr_;
         }

         inline token_t& next_token()
         {
            if (token_list_.end() != token_itr_)
            {
               return *token_itr_++;
            }
            else
               return eof_token_;
         }

         inline std::string error() const
         {
            return error_description_;
         }

      private:

         inline void skip_whitespace()
         {
            while ((s_end != s_itr) && is_whitespace(*s_itr))
            {
               ++s_itr;
            }
         }

         inline void scan_token()
         {
            skip_whitespace();

            if (s_end == s_itr)
            {
               return;
            }
            else if (is_operator_char(*s_itr))
            {
               scan_operator();
               return;
            }
            else if (is_letter(*s_itr))
            {
               scan_symbol();
               return;
            }
            else if (is_digit((*s_itr)) || ('.' == (*s_itr)))
            {
               scan_number();
               return;
            }
            else if ('$' == (*s_itr))
            {
               scan_special_function();
               return;
            }
            #ifndef exprtk_disable_string_capabilities
            else if ('\'' == (*s_itr))
            {
               scan_string();
               return;
            }
            #endif
            else
            {
               set_error(std::string("scan_token() - error invalid token: ") + std::string(s_itr,s_itr + 2));
               token_list_.push_back(error(s_itr,s_itr + 1));
               ++s_itr;
            }
         }

         inline void scan_operator()
         {
            if ((s_itr + 1) != s_end)
            {
               typename token_t::token_type ttype = token_t::none;
               char c0 = s_itr[0];
               char c1 = s_itr[1];
                    if ((c0 == '<') && (c1 == '=')) ttype = token_t::lte;
               else if ((c0 == '>') && (c1 == '=')) ttype = token_t::gte;
               else if ((c0 == '<') && (c1 == '>')) ttype = token_t::ne;
               else if ((c0 == '!') && (c1 == '=')) ttype = token_t::ne;
               else if ((c0 == '=') && (c1 == '=')) ttype = token_t::eq;
               else if ((c0 == ':') && (c1 == '=')) ttype = token_t::assign;
               else if ((c0 == '<') && (c1 == '<')) ttype = token_t::shl;
               else if ((c0 == '>') && (c1 == '>')) ttype = token_t::shr;
               if (token_t::none != ttype)
               {
                  token_list_.push_back(token_t(ttype));
                  s_itr += 2;
                  return;
               }
            }
                 if ('<' == *s_itr) token_list_.push_back(token_t(token_t::lt));
            else if ('>' == *s_itr) token_list_.push_back(token_t(token_t::gt));
            else
               token_list_.push_back(token_t(typename token_t::token_type((*s_itr))));
            ++s_itr;
         }

         inline void scan_symbol()
         {
            const char* begin = s_itr;
            while ((s_end != s_itr) &&
                   (is_letter((*s_itr)) || is_digit ((*s_itr)) || ((*s_itr) == '_')))
            {
               ++s_itr;
            }
            static const std::string true_string  = "true";
            static const std::string false_string = "false";
            if (details::imatch(std::string(begin,s_itr),true_string))
               token_list_.push_back(token_t(token_t::number,T(1)));
            else if (details::imatch(std::string(begin,s_itr),false_string))
               token_list_.push_back(token_t(token_t::number,T(0)));
            else
               token_list_.push_back(token_t(token_t::symbol,begin,s_itr));
         }

         inline void scan_number()
         {
            /*
               Attempt to match a valid numeric value in one of the following formats:
               1. 123456
               2. 123.456
               3. 123.456e3
               4. 123.456E3
               5. 123.456e+3
               6. 123.456E+3
               7. 123.456e-3
               8. 123.456E-3
            */
            const char* begin = s_itr;
            bool dot_found = false;
            bool e_found = false;
            bool post_e_sign_found = false;
            while (s_end != s_itr)
            {
              if ('.' == (*s_itr))
              {
                 if (dot_found)
                 {
                    set_error(std::string("scan_number() - error invalid numeric token[1]: ") + std::string(begin,s_itr));
                    token_list_.push_back(error(begin,s_itr));
                    return;
                 }
                 dot_found = true;
                 ++s_itr;
                 continue;
              }
              else if (imatch('e',(*s_itr)))
              {
                 const char& c = *(s_itr + 1);
                 if (s_end == (s_itr + 1))
                 {
                    set_error(std::string("scan_number() - error invalid numeric token[2]: ") + std::string(begin,s_itr));
                    token_list_.push_back(error(begin,s_itr));
                    return;
                 }
                 else if (('+' != c) && ('-' != c) && !is_digit(c))
                 {
                    set_error(std::string("scan_number() - error invalid numeric token[3]: ") + std::string(begin,s_itr));
                    token_list_.push_back(error(begin,s_itr));
                    return;
                 }
                 e_found = true;
                 ++s_itr;
                 continue;
              }
              else if (e_found && is_sign(*s_itr))
              {
                 if (post_e_sign_found)
                 {
                    set_error(std::string("scan_number() - error invalid numeric token[4]: ") + std::string(begin,s_itr));
                    token_list_.push_back(error(begin,s_itr));
                    return;
                 }
                 post_e_sign_found = true;
                 ++s_itr;
                 continue;
              }
              else if (('.' != (*s_itr)) && !is_digit(*s_itr))
                  break;
               else
                  ++s_itr;
            }
            T value = T(0.0);
            if (string_to_real(begin,s_itr,value))
               token_list_.push_back(token_t(token_t::number,value));
            else
            {
               set_error(std::string("scan_number() - error failed to parse token to real type. ") + std::string(begin,s_itr));
               token_list_.push_back(error(begin,s_itr));
            }
            return;
         }

         inline void scan_special_function()
         {
            const char* begin = s_itr;
            //$fdd(x,x,x) = 11 chars
            if (std::distance(s_itr,s_end) < 11)
            {
               set_error(std::string("scan_special_function() - error invalid special function [1]: ") + std::string(begin,s_itr));
               token_list_.push_back(error(begin,s_itr));
               return;
            }

            if (!(('$' == *s_itr)            &&
                  (imatch('f',*(s_itr + 1))) &&
                  ('(' == *(s_itr + 4))      &&
                  (is_digit(*(s_itr + 2)))   &&
                  (is_digit(*(s_itr + 3)))))
            {
               set_error(std::string("scan_special_function() - error invalid special function [2]: ") + std::string(begin,s_itr));
               token_list_.push_back(error(begin,s_itr));
               return;
            }
            s_itr += 4;
            token_list_.push_back(token_t(token_t::symbol,begin,s_itr));
            return;
         }

         #ifndef exprtk_disable_string_capabilities
         inline void scan_string()
         {
            const char* begin = s_itr + 1;
            if (std::distance(s_itr,s_end) < 2)
            {
               set_error(std::string("scan_string() - error invalid string [1]: ") + std::string(begin,s_itr));
               token_list_.push_back(error(begin,s_itr));
               return;
            }
            ++s_itr;
            bool escaped = false;
            std::string result_string;
            while (s_end != s_itr)
            {
               if ('\\' == *s_itr)
               {
                  escaped = true;
                  ++s_itr;
                  continue;
               }
               else if (!escaped)
               {
                  if ('\'' == *s_itr)
                     break;
               }
               else if (escaped)
                  escaped = false;
               result_string += *s_itr;
               ++s_itr;
            }
            if (s_end == s_itr)
            {
               set_error(std::string("scan_string() - error string has not been terminated: ") + std::string(begin,s_itr));
               token_list_.push_back(error(begin,s_itr));
               return;
            }
            token_list_.push_back(token_t(token_t::string,result_string));
            ++s_itr;
            return;
         }
         #endif

         inline void process_commutative_symbols()
         {
            if (token_list_.size() < 2)
               return;
            typename std::deque<token_t>::iterator itr = token_list_.begin() + 1;
            typename std::deque<token_t>::iterator prev_itr = token_list_.begin();
            while (token_list_.end() != itr)
            {
               token_t& curr_token = *itr;
               token_t& prev_token = *prev_itr;
               bool curr_token_not_reserved = !is_reserved_word(curr_token.value);
               if (
                    //3x -> 3*x
                    ((token_t::symbol == curr_token.type) && (token_t::number == prev_token.type) && curr_token_not_reserved) ||
                    //3(x+1) -> 3*(x+1)
                    (is_left_bracket (static_cast<char>(curr_token.type)) && (token_t::number == prev_token.type)) ||
                    //(x+1)3 -> (x+1)*3
                    (is_right_bracket(static_cast<char>(prev_token.type)) && (token_t::number == curr_token.type)) ||
                    //(x+1)y -> (x+1)*y
                    (is_right_bracket(static_cast<char>(prev_token.type)) && (token_t::symbol == curr_token.type) && curr_token_not_reserved)
                  )
               {
                  prev_itr = itr = token_list_.insert(itr,token_t(token_t::mul));
                  ++itr;
                  continue;
               }
               ++itr;
               ++prev_itr;
            }
         }

         inline void set_error(const std::string& s)
         {
            if (error_description_.empty())
            {
               error_description_ = s;
            }
         }

         inline token_t error(const char* begin, const char* end) const
         {
            return token_t(token_t::error,begin,end);
         }

      private:

         template <typename Iterator, typename Type>
         static inline bool string_to_type_converter_impl_ref(Iterator& itr, const Iterator end, Type& result)
         {
            if (end == itr) return false;

            Type t = 0;
            bool negative = false;

            if ('+' == (*itr))
               ++itr;
            else if ('-' == (*itr))
            {
               ++itr;
               negative = true;
            }

            if (end == itr)
               return false;

            unsigned int digit_count = 0;
            while ((end != itr) && ('0' == (*itr))) ++itr;

            bool return_result = true;
            while (end != itr)
            {
               const unsigned char digit = (*itr - '0');
               if (digit > 9)
               {
                  return_result = false;
                  break;
               }

               if ((++digit_count) <= numeric::numeric_info<Type>::bound_length)
               {
                  t *= 10;
                  t += digit;
               }
               else
               {
                  typedef unsigned long long int base_type;
                  static const base_type max_limit = +std::numeric_limits<Type>::max();
                  static const base_type min_limit = -std::numeric_limits<Type>::min();
                  base_type tmp = static_cast<base_type>(t) * 10 + digit;
                  if (negative && static_cast<base_type>(tmp) > min_limit)
                     return_result = false;
                  else if (static_cast<base_type>(tmp) > max_limit)
                     return_result = false;
                  t = static_cast<Type>(tmp);
               }
               ++itr;
            }

            result = static_cast<Type>((negative) ? -t : t);
            return return_result;
         }

         template <typename Iterator>
         static inline bool parse_nan(Iterator& itr, const Iterator end, T& t)
         {
            typedef typename std::iterator_traits<Iterator>::value_type type;
            static const std::size_t nan_length = 3;
            if (std::distance(itr,end) != static_cast<int>(nan_length))
               return false;
            if (static_cast<type>('n') == (*itr))
            {
               if ((static_cast<type>('a') != *(itr + 1)) || (static_cast<type>('n') != *(itr + 2)))
               {
                  return false;
               }
            }
            else if ((static_cast<type>('A') != *(itr + 1)) || (static_cast<type>('N') != *(itr + 2)))
            {
               return false;
            }
            t = std::numeric_limits<T>::quiet_NaN();
            return true;
         }

         template <typename Iterator>
         static inline bool parse_inf(Iterator& itr, const Iterator end, T& t, bool negative)
         {
            static const char inf_uc[] = "INFINITY";
            static const char inf_lc[] = "infinity";
            static const std::size_t inf_length = 8;
            const std::size_t length = std::distance(itr,end);
            if ((3 != length) && (inf_length != length))
               return false;
            const char* inf_itr = ('i' == (*itr)) ? inf_lc : inf_uc;
            while (end != itr)
            {
               if (*inf_itr == static_cast<char>(*itr))
               {
                  ++itr;
                  ++inf_itr;
                  continue;
               }
               else
                  return false;
            }
            if (negative)
               t = -std::numeric_limits<T>::infinity();
            else
               t =  std::numeric_limits<T>::infinity();
            return true;
         }

         template <typename Iterator>
         inline bool string_to_real(Iterator& itr_external, const Iterator end, T& t)
         {
            if (end == itr_external) return false;
            Iterator itr = itr_external;
            double d = 0.0;
            bool negative = false;
            if ('+' == (*itr))
               ++itr;
            else if ('-' == (*itr))
            {
               ++itr;
               negative = true;
            }

            if (end == itr)
               return false;

            if (('I' <= (*itr)) && ((*itr) <= 'n'))
            {
               if (('i' == (*itr)) || ('I' == (*itr)))
               {
                  return parse_inf(itr,end,t,negative);
               }
               else if (('n' == (*itr)) || ('N' == (*itr)))
               {
                  return parse_nan(itr,end,t);
               }
               else
                  return false;
            }

            bool instate = false;
            int pre_decimal = 0;

            if ('.' != (*itr))
            {
               const Iterator curr = itr;
               while ((end != itr) && ('0' == (*itr))) ++itr;
               const Iterator post_zero_cull_itr = itr;
               unsigned char digit = 0;

               #define parse_digit_1 \
               if ((digit = static_cast<unsigned char>((*itr) - '0')) < 10) { d *= 10.0; d += digit; } else break; if (end == ++itr) break; \

               #define parse_digit_2 \
               if ((digit = static_cast<unsigned char>((*itr) - '0')) < 10) { d *= 10.0; d += digit; } else break; ++itr;\

               while (end != itr)
               {
                  parse_digit_1
                  parse_digit_1
                  parse_digit_1
                  parse_digit_1
                  parse_digit_1
                  parse_digit_1
                  parse_digit_1
                  parse_digit_2
               }
               #undef parse_digit_1
               #undef parse_digit_2
               if (curr != itr) instate = true;
               pre_decimal = static_cast<int>(std::distance(post_zero_cull_itr,itr));
            }

            int exponent = 0;

            if (end != itr)
            {
               if ('.' == (*itr))
               {
                  ++itr;
                  const Iterator curr = itr;
                  unsigned char digit = 0;

                  #define parse_digit_1 \
                  if ((digit = static_cast<unsigned char>((*itr) - '0')) < 10) { d *= 10.0; d += digit; } else break; if (end == ++itr) break; \

                  #define parse_digit_2 \
                  if ((digit = static_cast<unsigned char>((*itr) - '0')) < 10) { d *= 10.0; d += digit; } else break; ++itr;\

                  while (end != itr)
                  {
                     parse_digit_1
                     parse_digit_1
                     parse_digit_1
                     parse_digit_1
                     parse_digit_1
                     parse_digit_1
                     parse_digit_1
                     parse_digit_2
                  }
                  #undef parse_digit_1
                  #undef parse_digit_2
                  if (curr != itr) instate = true;
                  exponent -= static_cast<int>(std::distance(curr,itr));
               }

               if (end != itr)
               {
                  typename std::iterator_traits<Iterator>::value_type c = (*itr);

                  if (('e' == c) || ('E' == c))
                  {
                     ++itr;
                     int exp = 0;
                     if (!string_to_type_converter_impl_ref(itr,end,exp))
                     {
                        if (end == itr)
                           return false;
                        else
                           c = (*itr);
                     }

                     if (
                         (exp < numeric::numeric_info<T>::min_exp) ||
                         (numeric::numeric_info<T>::max_exp < exp)
                        )
                        return false;

                     exponent += exp;
                  }

                  if (('f' == c) || ('F' == c) || ('l' == c) || ('L' == c))
                     ++itr;
                  else if ('#' == c)
                  {
                     ++itr;
                     if (end == itr)
                        return false;
                     if ((10.0 != d) || (exponent != -1))
                        return false;
                     if (('I' <= (*itr)) && ((*itr) <= 'n'))
                     {
                        if (('i' == (*itr)) || ('I' == (*itr)))
                        {
                           return parse_inf(itr,end,t,negative);
                        }
                        else if (('n' == (*itr)) || ('N' == (*itr)))
                        {
                           return parse_nan(itr,end,t);
                        }
                        else
                           return false;
                     }
                     return false;
                  }
               }
            }

            if ((end != itr) || (!instate))
               return false;

            if (0 != exponent)
            {
               if (
                  (std::numeric_limits<T>::max_exponent10 < (exponent + pre_decimal)) ||
                  (std::numeric_limits<T>::min_exponent10 > (exponent + pre_decimal))
                  )
               {
                  return false;
               }

               const int e = std::abs(exponent);
               static const double fract10[] =
                           {
                              0.0,
                              1.0E+001, 1.0E+002, 1.0E+003, 1.0E+004, 1.0E+005, 1.0E+006, 1.0E+007, 1.0E+008, 1.0E+009, 1.0E+010,
                              1.0E+011, 1.0E+012, 1.0E+013, 1.0E+014, 1.0E+015, 1.0E+016, 1.0E+017, 1.0E+018, 1.0E+019, 1.0E+020,
                              1.0E+021, 1.0E+022, 1.0E+023, 1.0E+024, 1.0E+025, 1.0E+026, 1.0E+027, 1.0E+028, 1.0E+029, 1.0E+030,
                              1.0E+031, 1.0E+032, 1.0E+033, 1.0E+034, 1.0E+035, 1.0E+036, 1.0E+037, 1.0E+038, 1.0E+039, 1.0E+040,
                              1.0E+041, 1.0E+042, 1.0E+043, 1.0E+044, 1.0E+045, 1.0E+046, 1.0E+047, 1.0E+048, 1.0E+049, 1.0E+050,
                              1.0E+051, 1.0E+052, 1.0E+053, 1.0E+054, 1.0E+055, 1.0E+056, 1.0E+057, 1.0E+058, 1.0E+059, 1.0E+060,
                              1.0E+061, 1.0E+062, 1.0E+063, 1.0E+064, 1.0E+065, 1.0E+066, 1.0E+067, 1.0E+068, 1.0E+069, 1.0E+070,
                              1.0E+071, 1.0E+072, 1.0E+073, 1.0E+074, 1.0E+075, 1.0E+076, 1.0E+077, 1.0E+078, 1.0E+079, 1.0E+080,
                              1.0E+081, 1.0E+082, 1.0E+083, 1.0E+084, 1.0E+085, 1.0E+086, 1.0E+087, 1.0E+088, 1.0E+089, 1.0E+090,
                              1.0E+091, 1.0E+092, 1.0E+093, 1.0E+094, 1.0E+095, 1.0E+096, 1.0E+097, 1.0E+098, 1.0E+099, 1.0E+100,
                              1.0E+101, 1.0E+102, 1.0E+103, 1.0E+104, 1.0E+105, 1.0E+106, 1.0E+107, 1.0E+108, 1.0E+109, 1.0E+110,
                              1.0E+111, 1.0E+112, 1.0E+113, 1.0E+114, 1.0E+115, 1.0E+116, 1.0E+117, 1.0E+118, 1.0E+119, 1.0E+120,
                              1.0E+121, 1.0E+122, 1.0E+123, 1.0E+124, 1.0E+125, 1.0E+126, 1.0E+127, 1.0E+128, 1.0E+129, 1.0E+130,
                              1.0E+131, 1.0E+132, 1.0E+133, 1.0E+134, 1.0E+135, 1.0E+136, 1.0E+137, 1.0E+138, 1.0E+139, 1.0E+140,
                              1.0E+141, 1.0E+142, 1.0E+143, 1.0E+144, 1.0E+145, 1.0E+146, 1.0E+147, 1.0E+148, 1.0E+149, 1.0E+150,
                              1.0E+151, 1.0E+152, 1.0E+153, 1.0E+154, 1.0E+155, 1.0E+156, 1.0E+157, 1.0E+158, 1.0E+159, 1.0E+160,
                              1.0E+161, 1.0E+162, 1.0E+163, 1.0E+164, 1.0E+165, 1.0E+166, 1.0E+167, 1.0E+168, 1.0E+169, 1.0E+170,
                              1.0E+171, 1.0E+172, 1.0E+173, 1.0E+174, 1.0E+175, 1.0E+176, 1.0E+177, 1.0E+178, 1.0E+179, 1.0E+180,
                              1.0E+181, 1.0E+182, 1.0E+183, 1.0E+184, 1.0E+185, 1.0E+186, 1.0E+187, 1.0E+188, 1.0E+189, 1.0E+190,
                              1.0E+191, 1.0E+192, 1.0E+193, 1.0E+194, 1.0E+195, 1.0E+196, 1.0E+197, 1.0E+198, 1.0E+199, 1.0E+200,
                              1.0E+221, 1.0E+222, 1.0E+223, 1.0E+224, 1.0E+225, 1.0E+226, 1.0E+227, 1.0E+228, 1.0E+229, 1.0E+230,
                              1.0E+231, 1.0E+232, 1.0E+233, 1.0E+234, 1.0E+235, 1.0E+236, 1.0E+237, 1.0E+238, 1.0E+239, 1.0E+240,
                              1.0E+241, 1.0E+242, 1.0E+243, 1.0E+244, 1.0E+245, 1.0E+246, 1.0E+247, 1.0E+248, 1.0E+249, 1.0E+250,
                              1.0E+251, 1.0E+252, 1.0E+253, 1.0E+254, 1.0E+255, 1.0E+256, 1.0E+257, 1.0E+258, 1.0E+259, 1.0E+260,
                              1.0E+261, 1.0E+262, 1.0E+263, 1.0E+264, 1.0E+265, 1.0E+266, 1.0E+267, 1.0E+268, 1.0E+269, 1.0E+270,
                              1.0E+271, 1.0E+272, 1.0E+273, 1.0E+274, 1.0E+275, 1.0E+276, 1.0E+277, 1.0E+278, 1.0E+279, 1.0E+280,
                              1.0E+281, 1.0E+282, 1.0E+283, 1.0E+284, 1.0E+285, 1.0E+286, 1.0E+287, 1.0E+288, 1.0E+289, 1.0E+290,
                              1.0E+291, 1.0E+292, 1.0E+293, 1.0E+294, 1.0E+295, 1.0E+296, 1.0E+297, 1.0E+298, 1.0E+299, 1.0E+300,
                              1.0E+301, 1.0E+302, 1.0E+303, 1.0E+304, 1.0E+305, 1.0E+306, 1.0E+307, 1.0E+308
                           };

               static const std::size_t fract10_size = sizeof(fract10) / sizeof(double);

               if (d != 0.0)
               {
                  if (static_cast<std::size_t>(e) < fract10_size)
                  {
                     if (exponent > 0)
                        d *= fract10[e];
                     else
                        d /= fract10[e];
                  }
                  else
                     d *= std::pow(10.0, 1.0 * exponent);
               }
            }

            t = static_cast<T>((negative) ? -d : d);
            return true;
         }

         std::string error_description_;
         std::deque<token_t> token_list_;
         typename std::deque<token_t>::iterator token_itr_;
         typename std::deque<token_t>::iterator store_token_itr_;
         token_t eof_token_;
         const char* s_itr;
         const char* s_end;
      };

      enum operator_type
      {
         e_default,
         e_add    ,
         e_sub    ,
         e_mul    ,
         e_div    ,
         e_mod    ,
         e_pow    ,
         e_atan2  ,
         e_min    ,
         e_max    ,
         e_avg    ,
         e_sum    ,
         e_prod   ,
         e_lt     ,
         e_lte    ,
         e_eq     ,
         e_equal  ,
         e_ne     ,
         e_nequal ,
         e_gte    ,
         e_gt     ,
         e_and    ,
         e_nand   ,
         e_or     ,
         e_nor    ,
         e_xor    ,
         e_shr    ,
         e_shl    ,
         e_abs    ,
         e_acos   ,
         e_asin   ,
         e_atan   ,
         e_ceil   ,
         e_cos    ,
         e_cosh   ,
         e_exp    ,
         e_floor  ,
         e_log    ,
         e_log10  ,
         e_logn   ,
         e_neg    ,
         e_pos    ,
         e_round  ,
         e_roundn ,
         e_root   ,
         e_sqrt   ,
         e_sin    ,
         e_sinh   ,
         e_sec    ,
         e_csc    ,
         e_tan    ,
         e_tanh   ,
         e_cot    ,
         e_clamp  ,
         e_inrange,
         e_sgn    ,
         e_r2d    ,
         e_d2r    ,
         e_d2g    ,
         e_g2d    ,
         e_hyp    ,
         e_notl   ,
         e_erf    ,
         e_erfc   ,
         e_assign ,
         e_in     ,
         e_like   ,
         e_ilike  ,

         // Do not add new functions/operators after this point.
         e_sf00 = 1000,
         e_sf01 = 1001,
         e_sf02 = 1002,
         e_sf03 = 1003,
         e_sf04 = 1004,
         e_sf05 = 1005,
         e_sf06 = 1006,
         e_sf07 = 1007,
         e_sf08 = 1008,
         e_sf09 = 1009,
         e_sf10 = 1010,
         e_sf11 = 1011,
         e_sf12 = 1012,
         e_sf13 = 1013,
         e_sf14 = 1014,
         e_sf15 = 1015,
         e_sf16 = 1016,
         e_sf17 = 1017,
         e_sf18 = 1018,
         e_sf19 = 1019,
         e_sf20 = 1020,
         e_sf21 = 1021,
         e_sf22 = 1022,
         e_sf23 = 1023,
         e_sf24 = 1024,
         e_sf25 = 1025,
         e_sf26 = 1026,
         e_sf27 = 1027,
         e_sf28 = 1028,
         e_sf29 = 1029,
         e_sf30 = 1030,
         e_sf31 = 1031,
         e_sf32 = 1032,
         e_sf33 = 1033,
         e_sf34 = 1034,
         e_sf35 = 1035,
         e_sf36 = 1036,
         e_sf37 = 1037,
         e_sf38 = 1038,
         e_sf39 = 1039,
         e_sf40 = 1040,
         e_sf41 = 1041,
         e_sf42 = 1042,
         e_sf43 = 1043,
         e_sf44 = 1044,
         e_sf45 = 1045,
         e_sf46 = 1046,
         e_sf47 = 1047,
         e_sf48 = 1048,
         e_sf49 = 1049,
         e_sf50 = 1050,
         e_sf51 = 1051,
         e_sf52 = 1052,
         e_sf53 = 1053,
         e_sf54 = 1054,
         e_sf55 = 1055,
         e_sf56 = 1056,
         e_sf57 = 1057,
         e_sf58 = 1058,
         e_sf59 = 1059,
         e_sf60 = 1060,
         e_sf61 = 1061,
         e_sf62 = 1062,
         e_sf63 = 1063,
         e_sf64 = 1064,
         e_sf65 = 1065,
         e_sf66 = 1066,
         e_sf67 = 1067,
         e_sf68 = 1068,
         e_sf69 = 1069,
         e_sf70 = 1070,
         e_sf71 = 1071,
         e_sf72 = 1072,
         e_sf73 = 1073,
         e_sf74 = 1074,
         e_sf75 = 1075,
         e_sf76 = 1076,
         e_sf77 = 1077,
         e_sf78 = 1078,
         e_sf79 = 1079,
         e_sf80 = 1080,
         e_sf81 = 1081,
         e_sf82 = 1082,
         e_sf83 = 1083
      };

      namespace numeric
      {
         namespace details
         {
            template <typename T>
            inline T process_impl(const operator_type operation, const T& arg, real_type_tag)
            {
               switch (operation)
               {
                  case e_abs   : return numeric::abs  (arg);
                  case e_acos  : return numeric::acos (arg);
                  case e_asin  : return numeric::asin (arg);
                  case e_atan  : return numeric::atan (arg);
                  case e_ceil  : return numeric::ceil (arg);
                  case e_cos   : return numeric::cos  (arg);
                  case e_cosh  : return numeric::cosh (arg);
                  case e_exp   : return numeric::exp  (arg);
                  case e_floor : return numeric::floor(arg);
                  case e_log   : return numeric::log  (arg);
                  case e_log10 : return numeric::log10(arg);
                  case e_neg   : return numeric::neg  (arg);
                  case e_pos   : return numeric::pos  (arg);
                  case e_round : return numeric::round(arg);
                  case e_sin   : return numeric::sin  (arg);
                  case e_sinh  : return numeric::sinh (arg);
                  case e_sqrt  : return numeric::sqrt (arg);
                  case e_tan   : return numeric::tan  (arg);
                  case e_tanh  : return numeric::tanh (arg);
                  case e_cot   : return numeric::cot  (arg);
                  case e_sec   : return numeric::sec  (arg);
                  case e_csc   : return numeric::csc  (arg);
                  case e_r2d   : return numeric::r2d  (arg);
                  case e_d2r   : return numeric::d2r  (arg);
                  case e_d2g   : return numeric::d2g  (arg);
                  case e_g2d   : return numeric::g2d  (arg);
                  case e_notl  : return numeric::notl (arg);
                  case e_sgn   : return numeric::sgn  (arg);
                  case e_erf   : return numeric::erf  (arg);
                  case e_erfc  : return numeric::erfc (arg);
                  default      : return std::numeric_limits<T>::quiet_NaN();
               }
            }

            template <typename T>
            inline T process_impl(const operator_type operation, const T& arg, int_type_tag)
            {
               switch (operation)
               {
                  case e_abs   : return numeric::abs  (arg);
                  case e_exp   : return numeric::exp  (arg);
                  case e_log   : return numeric::log  (arg);
                  case e_log10 : return numeric::log10(arg);
                  case e_neg   : return numeric::neg  (arg);
                  case e_pos   : return numeric::pos  (arg);
                  case e_sqrt  : return numeric::sqrt (arg);
                  case e_notl  : return numeric::notl (arg);
                  case e_sgn   : return numeric::sgn  (arg);
                  default      : return std::numeric_limits<T>::quiet_NaN();
               }
            }

            template <typename T>
            inline T process_impl(const operator_type operation, const T& arg0, const T& arg1, real_type_tag)
            {
               switch (operation)
               {
                  case e_add    : return (arg0 + arg1);
                  case e_sub    : return (arg0 - arg1);
                  case e_mul    : return (arg0 * arg1);
                  case e_div    : return (arg0 / arg1);
                  case e_mod    : return modulus<T>(arg0,arg1);
                  case e_pow    : return pow<T>(arg0,arg1);
                  case e_atan2  : return atan2<T>(arg0,arg1);
                  case e_min    : return std::min<T>(arg0,arg1);
                  case e_max    : return std::max<T>(arg0,arg1);
                  case e_logn   : return logn<T>(arg0,arg1);
                  case e_lt     : return (arg0 <  arg1) ? T(1) : T(0);
                  case e_lte    : return (arg0 <= arg1) ? T(1) : T(0);
                  case e_eq     : return (arg0 == arg1) ? T(1) : T(0);
                  case e_ne     : return (arg0 != arg1) ? T(1) : T(0);
                  case e_gte    : return (arg0 >= arg1) ? T(1) : T(0);
                  case e_gt     : return (arg0 >  arg1) ? T(1) : T(0);
                  case e_and    : return ((arg0 != T(0)) && (arg1 != T(0))) ? T(1) : T(0);
                  case e_nand   : return ((arg0 != T(0)) && (arg1 != T(0))) ? T(0) : T(1);
                  case e_or     : return ((arg0 != T(0)) || (arg1 != T(0))) ? T(1) : T(0);
                  case e_nor    : return ((arg0 != T(0)) || (arg1 != T(0))) ? T(0) : T(1);
                  case e_xor    : return (arg0 != arg1) ? T(1) : T(0);
                  case e_root   : return root<T>(arg0,arg1);
                  case e_roundn : return roundn<T>(arg0,arg1);
                  case e_equal  : return equal<T>(arg0,arg1);
                  case e_nequal : return nequal<T>(arg0,arg1);
                  case e_hyp    : return hyp<T>(arg0,arg1);
                  case e_avg    : return (arg0 + arg1)/T(2);
                  case e_sum    : return (arg0 + arg1);
                  case e_prod   : return (arg0 * arg1);
                  case e_shr    : return shr<T>(arg0,arg1);
                  case e_shl    : return shl<T>(arg0,arg1);
                  default       : return std::numeric_limits<T>::quiet_NaN();
               }
            }

            template <typename T>
            inline T process_impl(const operator_type operation, const T& arg0, const T& arg1, int_type_tag)
            {
               switch (operation)
               {
                  case e_add    : return (arg0 + arg1);
                  case e_sub    : return (arg0 - arg1);
                  case e_mul    : return (arg0 * arg1);
                  case e_div    : return (arg0 / arg1);
                  case e_mod    : return arg0 % arg1;
                  case e_pow    : return pow<T>(arg0,arg1);
                  case e_min    : return std::min<T>(arg0,arg1);
                  case e_max    : return std::max<T>(arg0,arg1);
                  case e_logn   : return logn<T>(arg0,arg1);
                  case e_lt     : return (arg0 <  arg1) ? T(1) : T(0);
                  case e_lte    : return (arg0 <= arg1) ? T(1) : T(0);
                  case e_eq     : return (arg0 == arg1) ? T(1) : T(0);
                  case e_ne     : return (arg0 != arg1) ? T(1) : T(0);
                  case e_gte    : return (arg0 >= arg1) ? T(1) : T(0);
                  case e_gt     : return (arg0 >  arg1) ? T(1) : T(0);
                  case e_and    : return ((arg0 != T(0)) && (arg1 != T(0))) ? T(1) : T(0);
                  case e_nand   : return ((arg0 != T(0)) && (arg1 != T(0))) ? T(0) : T(1);
                  case e_or     : return ((arg0 != T(0)) || (arg1 != T(0))) ? T(1) : T(0);
                  case e_nor    : return ((arg0 != T(0)) || (arg1 != T(0))) ? T(0) : T(1);
                  case e_xor    : return arg0 ^ arg1;
                  case e_root   : return root<T>(arg0,arg1);
                  case e_equal  : return arg0 == arg1;
                  case e_nequal : return arg0 != arg1;
                  case e_hyp    : return hyp<T>(arg0,arg1);
                  case e_avg    : return (arg0 + arg1) >> 1;
                  case e_sum    : return (arg0 + arg1);
                  case e_prod   : return (arg0 * arg1);
                  case e_shr    : return arg0 >> arg1;
                  case e_shl    : return arg0 << arg1;
                  default       : return std::numeric_limits<T>::quiet_NaN();
               }
            }
         }

         template <typename T>
         inline T process(const operator_type operation, const T& arg)
         {
            typename details::number_type<T>::type num_type;
            return details::process_impl<T>(operation,arg,num_type);
         }

         template <typename T>
         inline T process(const operator_type operation, const T& arg0, const T& arg1)
         {
            typename details::number_type<T>::type num_type;
            return details::process_impl<T>(operation,arg0,arg1,num_type);
         }
      }

      template <typename T>
      class expression_node
      {
      public:

         enum node_type
         {
            e_none        ,
            e_constant    ,
            e_unary       ,
            e_binary      ,
            e_trinary     ,
            e_quaternary  ,
            e_quinary     ,
            e_senary      ,
            e_conditional ,
            e_while       ,
            e_variable    ,
            e_stringvar   ,
            e_stringconst ,
            e_function    ,
            e_add         ,
            e_sub         ,
            e_mul         ,
            e_div         ,
            e_mod         ,
            e_pow         ,
            e_lt          ,
            e_lte         ,
            e_gt          ,
            e_gte         ,
            e_eq          ,
            e_ne          ,
            e_and         ,
            e_nand        ,
            e_or          ,
            e_nor         ,
            e_xor         ,
            e_in          ,
            e_like        ,
            e_ilike       ,
            e_inranges    ,
            e_ipow        ,
            e_vov         ,
            e_abs         ,
            e_acos        ,
            e_asin        ,
            e_atan        ,
            e_ceil        ,
            e_cos         ,
            e_cosh        ,
            e_exp         ,
            e_floor       ,
            e_log         ,
            e_log10       ,
            e_neg         ,
            e_pos         ,
            e_round       ,
            e_sin         ,
            e_sinh        ,
            e_sqrt        ,
            e_tan         ,
            e_tanh        ,
            e_cot         ,
            e_sec         ,
            e_csc         ,
            e_r2d         ,
            e_d2r         ,
            e_d2g         ,
            e_g2d         ,
            e_notl        ,
            e_sgn         ,
            e_erf         ,
            e_erfc
         };

         typedef T value_type;
         typedef expression_node<T>* expression_ptr;

         virtual ~expression_node()
         {}

         virtual inline T value() const
         {
            return std::numeric_limits<T>::quiet_NaN();
         }

         virtual inline bool result() const
         {
            return (T(1.0) == value());
         }

         virtual inline expression_node<T>* branch(const std::size_t& index = 0) const
         {
            return reinterpret_cast<expression_ptr>(index * 0);
         }

         virtual inline node_type type() const
         {
            return e_none;
         }
      };

      template <typename T>
      inline bool is_unary_node(const expression_node<T>* node)
      {
         return (details::expression_node<T>::e_unary == node->type());
      }

      template <typename T>
      inline bool is_binary_node(const expression_node<T>* node)
      {
         return (details::expression_node<T>::e_binary == node->type());
      }

      template <typename T>
      inline bool is_variable_node(const expression_node<T>* node)
      {
         return (details::expression_node<T>::e_variable == node->type());
      }

      template <typename T>
      inline bool is_constant_node(const expression_node<T>* node)
      {
         return (details::expression_node<T>::e_constant == node->type());
      }

      template <typename T>
      inline bool is_function(const expression_node<T>* node)
      {
         return (details::expression_node<T>::e_function == node->type());
      }

      template <typename T>
      inline bool branch_deletable(expression_node<T>* node)
      {
         return !is_variable_node(node);
      }

      template <typename T>
      class literal_node : public expression_node<T>
      {
      public:

         explicit literal_node(const T& value)
         : value_(value)
         {}

         inline T value() const
         {
            return value_;
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_constant;
         }

         inline expression_node<T>* branch(const std::size_t& index = 0) const
         {
            return reinterpret_cast<expression_node<T>*>(index * 0);
         }

      private:

         T value_;
      };

      template <typename T>
      class string_literal_node : public expression_node<T>
      {
      public:

         explicit string_literal_node(const std::string& value)
         : value_(value)
         {}

         inline T value() const
         {
            return std::numeric_limits<T>::quiet_NaN();
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_stringconst;
         }

         inline expression_node<T>* branch(const std::size_t& index = 0) const
         {
            return reinterpret_cast<expression_node<T>*>(index * 0);
         }

         inline std::string str()
         {
            return value_;
         }

      private:

         string_literal_node(const string_literal_node<T>&);
         string_literal_node<T>& operator=(const string_literal_node<T>&);

         const std::string value_;
      };

      template <typename T>
      class unary_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;

         unary_node(const operator_type& operation,
                    expression_ptr branch)
         : operation_(operation),
           branch_(branch),
           branch_deletable_(branch_deletable(branch_))
         {}

        ~unary_node()
         {
            if (branch_ && branch_deletable_)
            {
               delete branch_;
               branch_ = 0;
            }
         }

         inline T value() const
         {
            const T arg = branch_->value();
            return numeric::process<T>(operation_,arg);
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_unary;
         }

         inline operator_type operation() const
         {
            return operation_;
         }

         inline expression_node<T>* branch(const std::size_t& index = 0) const
         {
            if (0 == index)
               return branch_;
            else
               return reinterpret_cast<expression_ptr>(0);
         }

      private:

         operator_type operation_;
         expression_ptr branch_;
         bool           branch_deletable_;
      };

      template <typename T, std::size_t D, bool B>
      struct construct_branch_pair
      {
         template <std::size_t N>
         static inline void process(std::pair<expression_node<T>*,bool> (&)[N], expression_node<T>*)
         {}
      };

      template <typename T, std::size_t D>
      struct construct_branch_pair<T,D,true>
      {
         template <std::size_t N>
         static inline void process(std::pair<expression_node<T>*,bool> (&branch)[N], expression_node<T>* b)
         { if (b) branch[D] = std::make_pair(b,branch_deletable(b)); }
      };

      template <std::size_t N, typename T>
      inline void init_branches(std::pair<expression_node<T>*,bool> (&branch)[N],
                                expression_node<T>* b0,
                                expression_node<T>* b1 = reinterpret_cast<expression_node<T>*>(0),
                                expression_node<T>* b2 = reinterpret_cast<expression_node<T>*>(0),
                                expression_node<T>* b3 = reinterpret_cast<expression_node<T>*>(0),
                                expression_node<T>* b4 = reinterpret_cast<expression_node<T>*>(0),
                                expression_node<T>* b5 = reinterpret_cast<expression_node<T>*>(0),
                                expression_node<T>* b6 = reinterpret_cast<expression_node<T>*>(0),
                                expression_node<T>* b7 = reinterpret_cast<expression_node<T>*>(0),
                                expression_node<T>* b8 = reinterpret_cast<expression_node<T>*>(0),
                                expression_node<T>* b9 = reinterpret_cast<expression_node<T>*>(0))
      {
         construct_branch_pair<T,0,(N > 0)>::process(branch,b0);
         construct_branch_pair<T,1,(N > 1)>::process(branch,b1);
         construct_branch_pair<T,2,(N > 2)>::process(branch,b2);
         construct_branch_pair<T,3,(N > 3)>::process(branch,b3);
         construct_branch_pair<T,4,(N > 4)>::process(branch,b4);
         construct_branch_pair<T,5,(N > 5)>::process(branch,b5);
         construct_branch_pair<T,6,(N > 6)>::process(branch,b6);
         construct_branch_pair<T,7,(N > 7)>::process(branch,b7);
         construct_branch_pair<T,8,(N > 8)>::process(branch,b8);
         construct_branch_pair<T,9,(N > 9)>::process(branch,b9);
      }

      template <typename T, std::size_t N>
      struct cleanup_branches
      {
         static inline void execute(std::pair<expression_node<T>*,bool> (&branch)[N])
         {
            for (std::size_t i = 0; i < N; ++i)
            {
               if (branch[i].first && branch[i].second)
               {
                  delete branch[i].first;
                  branch[i].first = 0;
               }
            }
         }
      };

      template <typename T>
      class binary_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef std::pair<expression_ptr,bool> branch_t;

         binary_node(const operator_type& operation,
                     expression_ptr branch0,
                     expression_ptr branch1)
         : operation_(operation)
         {
            init_branches<2>(branch_,branch0,branch1);
         }

        ~binary_node()
         {
            cleanup_branches<T,2>::execute(branch_);
         }

         inline T value() const
         {
            const T arg0 = branch_[0].first->value();
            const T arg1 = branch_[1].first->value();
            return numeric::process<T>(operation_,arg0,arg1);
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_binary;
         }

         inline operator_type operation() const
         {
            return operation_;
         }

         inline expression_node<T>* branch(const std::size_t& index = 0) const
         {
            if (0 == index)
               return branch_[0].first;
            else if (1 == index)
               return branch_[1].first;
            else
               return reinterpret_cast<expression_ptr>(0);
         }

      protected:

         operator_type operation_;
         branch_t branch_[2];
      };

      template <typename T>
      class trinary_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef std::pair<expression_ptr,bool> branch_t;

         trinary_node(const operator_type& operation,
                      expression_ptr branch0,
                      expression_ptr branch1,
                      expression_ptr branch2)
         : operation_(operation)
         {
            init_branches<3>(branch_,branch0,branch1,branch2);
         }

        ~trinary_node()
         {
            cleanup_branches<T,3>::execute(branch_);
         }

         inline T value() const
         {
            const T arg0 = branch_[0].first->value();
            const T arg1 = branch_[1].first->value();
            const T arg2 = branch_[2].first->value();
            switch (operation_)
            {
               case e_clamp   : return (arg1 < arg0) ? arg0 : (arg1 > arg2 ? arg2 : arg1);
               case e_inrange : return (arg1 < arg0) ? T(0) : ((arg1 > arg2) ? T(0) : T(1));
               case e_min     : return std::min<T>(std::min<T>(arg0,arg1),arg2);
               case e_max     : return std::max<T>(std::max<T>(arg0,arg1),arg2);
               case e_avg     : return (arg0 + arg1 + arg2) / T(3.0);
               case e_sum     : return (arg0 + arg1 + arg2);
               case e_prod    : return (arg0 * arg1 * arg2);
               default        : return std::numeric_limits<T>::quiet_NaN();
            }
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_trinary;
         }

      protected:

         operator_type operation_;
         branch_t branch_[3];
      };

      template <typename T>
      class quaternary_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef std::pair<expression_ptr,bool> branch_t;

         quaternary_node(const operator_type& operation,
                         expression_ptr branch0,
                         expression_ptr branch1,
                         expression_ptr branch2,
                         expression_ptr branch3)
         : operation_(operation)
         {
            init_branches<4>(branch_,branch0,branch1,branch2,branch3);
         }

        ~quaternary_node()
         {
            cleanup_branches<T,4>::execute(branch_);
         }

         inline T value() const
         {
            const T arg0 = branch_[0].first->value();
            const T arg1 = branch_[1].first->value();
            const T arg2 = branch_[2].first->value();
            const T arg3 = branch_[3].first->value();
            switch (operation_)
            {
               case e_min  : return std::min<T>(std::min<T>(arg0,arg1),std::min<T>(arg2,arg3));
               case e_max  : return std::max<T>(std::max<T>(arg0,arg1),std::max<T>(arg2,arg3));
               case e_avg  : return (arg0 + arg1 + arg2 + arg3) / T(4.0);
               case e_sum  : return (arg0 + arg1 + arg2 + arg3);
               case e_prod : return (arg0 * arg1 * arg2 * arg3);
               default     : return std::numeric_limits<T>::quiet_NaN();
            }
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_quaternary;
         }

      protected:

         operator_type operation_;
         branch_t branch_[4];
      };

      template <typename T>
      class quinary_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef std::pair<expression_ptr,bool> branch_t;

         quinary_node(const operator_type& operation,
                      expression_ptr branch0,
                      expression_ptr branch1,
                      expression_ptr branch2,
                      expression_ptr branch3,
                      expression_ptr branch4)
         : operation_(operation)
         {
            init_branches<5>(branch_,branch0,branch1,branch2,branch3,branch4);
         }

        ~quinary_node()
         {
            cleanup_branches<T,5>::execute(branch_);
         }

         inline T value() const
         {
            const T arg0 = branch_[0].first->value();
            const T arg1 = branch_[1].first->value();
            const T arg2 = branch_[2].first->value();
            const T arg3 = branch_[3].first->value();
            const T arg4 = branch_[4].first->value();
            switch (operation_)
            {
               case e_min  : return std::min<T>(std::min<T>(std::min<T>(arg0,arg1),std::min<T>(arg2,arg3)),arg4);
               case e_max  : return std::max<T>(std::max<T>(std::max<T>(arg0,arg1),std::max<T>(arg2,arg3)),arg4);
               case e_avg  : return (arg0 + arg1 + arg2 + arg3 + arg4) / T(5.0);
               case e_sum  : return (arg0 + arg1 + arg2 + arg3 + arg4);
               case e_prod : return (arg0 * arg1 * arg2 * arg3 * arg4);
               default     : return std::numeric_limits<T>::quiet_NaN();
            }
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_quinary;
         }

      private:

         operator_type operation_;
         branch_t branch_[5];
      };

      template <typename T>
      class senary_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef std::pair<expression_ptr,bool> branch_t;

         senary_node(const operator_type& operation,
                     expression_ptr branch0,
                     expression_ptr branch1,
                     expression_ptr branch2,
                     expression_ptr branch3,
                     expression_ptr branch4,
                     expression_ptr branch5)
         : operation_(operation)
         {
            init_branches<6>(branch_,branch0,branch1,branch2,branch3,branch4,branch5);
         }

        ~senary_node()
         {
            cleanup_branches<T,6>::execute(branch_);
         }

         inline T value() const
         {
            const T arg0 = branch_[0].first->value();
            const T arg1 = branch_[1].first->value();
            const T arg2 = branch_[2].first->value();
            const T arg3 = branch_[3].first->value();
            const T arg4 = branch_[4].first->value();
            const T arg5 = branch_[5].first->value();
            switch (operation_)
            {
               case e_min     : return std::min<T>(std::min<T>(std::min<T>(arg0,arg1),std::min<T>(arg2,arg3)),std::min<T>(arg4,arg5));
               case e_max     : return std::max<T>(std::max<T>(std::max<T>(arg0,arg1),std::max<T>(arg2,arg3)),std::max<T>(arg4,arg5));
               case e_avg     : return (arg0 + arg1 + arg2 + arg3 + arg4 + arg5) / T(6.0);
               case e_sum     : return (arg0 + arg1 + arg2 + arg3 + arg4 + arg5);
               case e_prod    : return (arg0 * arg1 * arg2 * arg3 * arg4 * arg5);
               case e_default :
               default        : return std::numeric_limits<T>::quiet_NaN();
            }
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_senary;
         }

      private:

         operator_type operation_;
         branch_t branch_[6];
      };

      template <typename T>
      class conditional_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;

         conditional_node(expression_ptr test,
                          expression_ptr consequent,
                          expression_ptr alternative)
         : test_(test),
           consequent_(consequent),
           alternative_(alternative),
           test_deletable_(!is_variable_node(test_)),
           consequent_deletable_(!is_variable_node(consequent_)),
           alternative_deletable_(!is_variable_node(alternative_))
         {}

        ~conditional_node()
         {
            if (test_        &&        test_deletable_) delete test_;
            if (consequent_  &&  consequent_deletable_) delete consequent_;
            if (alternative_ && alternative_deletable_) delete alternative_;
         }

         inline T value() const
         {
            if (test_->value() != 0)
               return consequent_->value();
            else
               return alternative_->value();
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_conditional;
         }

      private:

         expression_ptr test_;
         expression_ptr consequent_;
         expression_ptr alternative_;
         bool test_deletable_;
         bool consequent_deletable_;
         bool alternative_deletable_;
      };

      template <typename T>
      class while_loop_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;

         while_loop_node(expression_ptr test,
                         expression_ptr branch)
         : test_(test),
           branch_(branch),
           test_deletable_(!is_variable_node(test_)),
           branch_deletable_(!is_variable_node(branch_))
         {}

        ~while_loop_node()
         {
            if (test_   &&   test_deletable_) delete test_;
            if (branch_ && branch_deletable_) delete branch_;
         }

         inline T value() const
         {
            T result = T(0);
            while (test_->value() != T(0))
            {
               result = branch_->value();
            }
            return result;
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_while;
         }

      private:

         expression_ptr test_;
         expression_ptr branch_;
         bool test_deletable_;
         bool branch_deletable_;
      };

      template <typename T>
      class variable_node : public expression_node<T>
      {
      public:

         static T null_value;

         explicit variable_node()
         : value_(&null_value)
         {}

         explicit variable_node(T& value)
         : value_(&value)
         {}

         inline bool operator <(const variable_node<T>& v) const
         {
            return this < (&v);
         }

         inline T value() const
         {
            return (*value_);
         }

         inline T& ref()
         {
            return (*value_);
         }

         inline const T& ref() const
         {
            return (*value_);
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_variable;
         }

      private:

         T* value_;
      };

      template <typename T>
      T variable_node<T>::null_value = T(std::numeric_limits<T>::quiet_NaN());

      #ifndef exprtk_disable_string_capabilities
      template <typename T>
      class stringvar_node : public expression_node<T>
      {
      public:

         static std::string null_value;

         explicit stringvar_node()
         : value_(&null_value)
         {}

         explicit stringvar_node(std::string& value)
         : value_(&value)
         {}

         inline bool operator <(const stringvar_node<T>& v) const
         {
            return this < (&v);
         }

         inline T value() const
         {
            return std::numeric_limits<T>::quiet_NaN();
         }

         inline std::string str() const
         {
            return (*value_);
         }

         inline virtual std::string& ref()
         {
            return (*value_);
         }

         inline virtual const std::string& ref() const
         {
            return (*value_);
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_stringvar;
         }

      private:

         std::string* value_;
      };

      template <typename T>
      std::string stringvar_node<T>::null_value = std::string("");
      #endif

      template <typename T, std::size_t N> inline T axn(T a, T x)       { return a * exprtk::details::numeric::fast_exp<T,N>::result(x); } // a*x^n
      template <typename T, std::size_t N> inline T axnb(T a, T x, T b) { return a * exprtk::details::numeric::fast_exp<T,N>::result(x) + b; } // a*x^n+b

      template <typename T> struct sf00_op { static inline T process(const T& x, const T& y, const T& z) { return (x + y) / z; } };
      template <typename T> struct sf01_op { static inline T process(const T& x, const T& y, const T& z) { return (x + y) * z; } };
      template <typename T> struct sf02_op { static inline T process(const T& x, const T& y, const T& z) { return (x - y) / z; } };
      template <typename T> struct sf03_op { static inline T process(const T& x, const T& y, const T& z) { return (x - y) * z; } };
      template <typename T> struct sf04_op { static inline T process(const T& x, const T& y, const T& z) { return (x * y) + z; } };
      template <typename T> struct sf05_op { static inline T process(const T& x, const T& y, const T& z) { return (x * y) - z; } };
      template <typename T> struct sf06_op { static inline T process(const T& x, const T& y, const T& z) { return (x * y) / z; } };
      template <typename T> struct sf07_op { static inline T process(const T& x, const T& y, const T& z) { return (x * y) * z; } };
      template <typename T> struct sf08_op { static inline T process(const T& x, const T& y, const T& z) { return (x / y) + z; } };
      template <typename T> struct sf09_op { static inline T process(const T& x, const T& y, const T& z) { return (x / y) - z; } };
      template <typename T> struct sf10_op { static inline T process(const T& x, const T& y, const T& z) { return (x / y) / z; } };
      template <typename T> struct sf11_op { static inline T process(const T& x, const T& y, const T& z) { return (x / y) * z; } };
      template <typename T> struct sf12_op { static inline T process(const T& x, const T& y, const T& z) { return x / (y + z); } };
      template <typename T> struct sf13_op { static inline T process(const T& x, const T& y, const T& z) { return x / (y - z); } };
      template <typename T> struct sf14_op { static inline T process(const T& x, const T& y, const T& z) { return x / (y * z); } };
      template <typename T> struct sf15_op { static inline T process(const T& x, const T& y, const T& z) { return x / (y / z); } };
      template <typename T> struct sf16_op { static inline T process(const T& x, const T& y, const T& z) { return x - (y / z); } };
      template <typename T> struct sf17_op { static inline T process(const T& x, const T& y, const T& z) { return x - (y / z); } };
      template <typename T> struct sf18_op { static inline T process(const T& x, const T& y, const T& z) { return axnb<T,2>(x,y,z); } }; //x * y^2 + z
      template <typename T> struct sf19_op { static inline T process(const T& x, const T& y, const T& z) { return axnb<T,3>(x,y,z); } }; //x * y^3 + z
      template <typename T> struct sf20_op { static inline T process(const T& x, const T& y, const T& z) { return axnb<T,4>(x,y,z); } }; //x * y^4 + z
      template <typename T> struct sf21_op { static inline T process(const T& x, const T& y, const T& z) { return axnb<T,5>(x,y,z); } }; //x * y^5 + z
      template <typename T> struct sf22_op { static inline T process(const T& x, const T& y, const T& z) { return axnb<T,6>(x,y,z); } }; //x * y^6 + z
      template <typename T> struct sf23_op { static inline T process(const T& x, const T& y, const T& z) { return axnb<T,7>(x,y,z); } }; //x * y^7 + z
      template <typename T> struct sf24_op { static inline T process(const T& x, const T& y, const T& z) { return axnb<T,8>(x,y,z); } }; //x * y^8 + z
      template <typename T> struct sf25_op { static inline T process(const T& x, const T& y, const T& z) { return axnb<T,9>(x,y,z); } }; //x * y^9 + z
      template <typename T> struct sf26_op { static inline T process(const T& x, const T& y, const T& z) { return x * numeric::log(y)   + z; } };
      template <typename T> struct sf27_op { static inline T process(const T& x, const T& y, const T& z) { return x * numeric::log(y)   - z; } };
      template <typename T> struct sf28_op { static inline T process(const T& x, const T& y, const T& z) { return x * numeric::log10(y) + z; } };
      template <typename T> struct sf29_op { static inline T process(const T& x, const T& y, const T& z) { return x * numeric::log10(y) - z; } };
      template <typename T> struct sf30_op { static inline T process(const T& x, const T& y, const T& z) { return x * numeric::sin(y) + z; } };
      template <typename T> struct sf31_op { static inline T process(const T& x, const T& y, const T& z) { return x * numeric::sin(y) - z; } };
      template <typename T> struct sf32_op { static inline T process(const T& x, const T& y, const T& z) { return x * numeric::cos(y) + z; } };
      template <typename T> struct sf33_op { static inline T process(const T& x, const T& y, const T& z) { return x * numeric::cos(y) - z; } };
      template <typename T> struct sf34_op { static inline T process(const T& x, const T& y, const T& z) { return (T(0) != x) ? y : z; } };
      template <typename T> struct sf35_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x + ((y + z) / w); } };
      template <typename T> struct sf36_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x + ((y + z) * w); } };
      template <typename T> struct sf37_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x + ((y - z) / w); } };
      template <typename T> struct sf38_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x + ((y - z) * w); } };
      template <typename T> struct sf39_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x + ((y * z) / w); } };
      template <typename T> struct sf40_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x + ((y * z) * w); } };
      template <typename T> struct sf41_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x + ((y / z) + w); } };
      template <typename T> struct sf42_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x + ((y / z) / w); } };
      template <typename T> struct sf43_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x + ((y / z) * w); } };
      template <typename T> struct sf44_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x - ((y + z) / w); } };
      template <typename T> struct sf45_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x - ((y + z) * w); } };
      template <typename T> struct sf46_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x - ((y - z) / w); } };
      template <typename T> struct sf47_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x - ((y - z) * w); } };
      template <typename T> struct sf48_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x - ((y * z) / w); } };
      template <typename T> struct sf49_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x - ((y * z) * w); } };
      template <typename T> struct sf50_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x - ((y / z) / w); } };
      template <typename T> struct sf51_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x - ((y / z) * w); } };
      template <typename T> struct sf52_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return ((x + y) * z) - w; } };
      template <typename T> struct sf53_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return ((x - y) * z) - w; } };
      template <typename T> struct sf54_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return ((x * y) * z) - w; } };
      template <typename T> struct sf55_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return ((x / y) * z) - w; } };
      template <typename T> struct sf56_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return ((x + y) / z) - w; } };
      template <typename T> struct sf57_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return ((x - y) / z) - w; } };
      template <typename T> struct sf58_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return ((x * y) / z) - w; } };
      template <typename T> struct sf59_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return ((x / y) / z) - w; } };
      template <typename T> struct sf60_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return (x * y) + (z * w); } };
      template <typename T> struct sf61_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return (x * y) - (z * w); } };
      template <typename T> struct sf62_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return (x * y) + (z / w); } };
      template <typename T> struct sf63_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return (x * y) - (z / w); } };
      template <typename T> struct sf64_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return (x / y) + (z / w); } };
      template <typename T> struct sf65_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return (x / y) - (z / w); } };
      template <typename T> struct sf66_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return (x / y) - (z / w); } };
      template <typename T> struct sf67_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return (x / y) - (z * w); } };
      template <typename T> struct sf68_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return axn<T,2>(x,y) + axn<T,2>(z,w); } }; //x*y^2+z*w^2
      template <typename T> struct sf69_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return axn<T,3>(x,y) + axn<T,3>(z,w); } }; //x*y^3+z*w^3
      template <typename T> struct sf70_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return axn<T,4>(x,y) + axn<T,4>(z,w); } }; //x*y^4+z*w^4
      template <typename T> struct sf71_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return axn<T,5>(x,y) + axn<T,5>(z,w); } }; //x*y^5+z*w^5
      template <typename T> struct sf72_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return axn<T,6>(x,y) + axn<T,6>(z,w); } }; //x*y^6+z*w^6
      template <typename T> struct sf73_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return axn<T,7>(x,y) + axn<T,7>(z,w); } }; //x*y^7+z*w^7
      template <typename T> struct sf74_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return axn<T,8>(x,y) + axn<T,8>(z,w); } }; //x*y^8+z*w^8
      template <typename T> struct sf75_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return axn<T,9>(x,y) + axn<T,9>(z,w); } }; //x*y^9+z*w^9
      template <typename T> struct sf76_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return ((T(0) != x) && (T(0) != y)) ? z : w; } };
      template <typename T> struct sf77_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return ((T(0) != x) || (T(0) != y)) ? z : w; } };
      template <typename T> struct sf78_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return (x <  y) ? z : w; } };
      template <typename T> struct sf79_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return (x <= y) ? z : w; } };
      template <typename T> struct sf80_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return (x >  y) ? z : w; } };
      template <typename T> struct sf81_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return (x >= y) ? z : w; } };
      template <typename T> struct sf82_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return numeric::equal(x,y) ? z : w; } };
      template <typename T> struct sf83_op { static inline T process(const T& x, const T& y, const T& z, const T& w) { return x * numeric::sin(y) + z * numeric::cos(w); } };

      template <typename T, typename SpecialFunction>
      class sf3_node : public trinary_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;

         sf3_node(const operator_type& operation,
                  expression_ptr branch0,
                  expression_ptr branch1,
                  expression_ptr branch2)
         : trinary_node<T>(operation,branch0,branch1,branch2)
         {}

         inline T value() const
         {
            const T x = trinary_node<T>::branch_[0].first->value();
            const T y = trinary_node<T>::branch_[1].first->value();
            const T z = trinary_node<T>::branch_[2].first->value();
            return SpecialFunction::process(x,y,z);
         }
      };

      template <typename T, typename SpecialFunction>
      class sf4_node : public quaternary_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;

         sf4_node(const operator_type& operation,
                  expression_ptr branch0,
                  expression_ptr branch1,
                  expression_ptr branch2,
                  expression_ptr branch3)
         : quaternary_node<T>(operation,branch0,branch1,branch2,branch3)
         {}

         inline T value() const
         {
            const T x = quaternary_node<T>::branch_[0].first->value();
            const T y = quaternary_node<T>::branch_[1].first->value();
            const T z = quaternary_node<T>::branch_[2].first->value();
            const T w = quaternary_node<T>::branch_[3].first->value();
            return SpecialFunction::process(x,y,z,w);
         }
      };

      template <typename T>
      class assignment_node : public binary_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;

         assignment_node(const operator_type& operation,
                         expression_ptr branch0,
                         expression_ptr branch1)
         : binary_node<T>(operation,branch0,branch1)
         {}

         inline T value() const
         {
            if (is_variable_node(binary_node<T>::branch_[0].first))
            {
               variable_node<T>* var_node_ptr = dynamic_cast<variable_node<T>*>(binary_node<T>::branch_[0].first);
               if (var_node_ptr)
               {
                  T& result = var_node_ptr->ref();
                  result = binary_node<T>::branch_[1].first->value();
                  return result;
               }
            }
            return std::numeric_limits<T>::quiet_NaN();
         }
      };

      template <typename T, typename IFunction, std::size_t N>
      class function_N_node : public expression_node<T>
      {
      public:
         //function of N paramters.
         typedef expression_node<T>* expression_ptr;
         typedef std::pair<expression_ptr,bool> branch_t;
         typedef IFunction ifunction;

         function_N_node(ifunction* func)
         : function_((N == func->param_count) ? func : reinterpret_cast<ifunction*>(0)),
           parameter_count_(func->param_count)
         {}

        ~function_N_node()
         {
            cleanup_branches<T,N>::execute(branch_);
         }

         template <std::size_t NumBranches>
         bool init_branches(expression_ptr (&b)[NumBranches])
         {
            //Needed for incompetent and broken msvc compiler versions
            #ifdef _MSC_VER
             #pragma warning(push)
             #pragma warning(disable: 4127)
            #endif
            if (N != NumBranches)
               return false;
            else
            {
               for (std::size_t i = 0; i < NumBranches; ++i)
               {
                  if (b[i])
                     branch_[i] = std::make_pair(b[i],branch_deletable(b[i]));
                  else
                     return false;
               }
               return true;
            }
            #ifdef _MSC_VER
             #pragma warning(pop)
            #endif
         }

         inline bool operator <(const function_N_node<T,IFunction,N>& fn) const
         {
            return this < (&fn);
         }

         inline T value() const
         {
            //Needed for incompetent and broken msvc compiler versions
            #ifdef _MSC_VER
             #pragma warning(push)
             #pragma warning(disable: 4127)
            #endif
            if ((0 == function_) || (0 == N))
               return std::numeric_limits<T>::quiet_NaN();
            else
            {
               T v[N];
               evaluate_branches<T,N>::execute(v,branch_);
               return invoke<T,N>::execute(*function_,v);
            }
            #ifdef _MSC_VER
             #pragma warning(pop)
            #endif
         }

         template <typename T_, std::size_t BranchCount>
         struct evaluate_branches
         {
            static inline void execute(T_ (&v)[BranchCount], const branch_t (&b)[BranchCount])
            {
               for (std::size_t i = 0; i < BranchCount; ++i)
               {
                  v[i] = b[i].first->value();
               }
            }
         };

         template <typename T_>
         struct evaluate_branches <T_,5>
         {
            static inline void execute(T_ (&v)[5], const branch_t (&b)[5])
            {
               v[0] = b[0].first->value();
               v[1] = b[1].first->value();
               v[2] = b[2].first->value();
               v[3] = b[3].first->value();
               v[4] = b[4].first->value();
            }
         };

         template <typename T_>
         struct evaluate_branches <T_,4>
         {
            static inline void execute(T_ (&v)[4], const branch_t (&b)[4])
            {
               v[0] = b[0].first->value();
               v[1] = b[1].first->value();
               v[2] = b[2].first->value();
               v[3] = b[3].first->value();
            }
         };

         template <typename T_>
         struct evaluate_branches <T_,3>
         {
            static inline void execute(T_ (&v)[3], const branch_t (&b)[3])
            {
               v[0] = b[0].first->value();
               v[1] = b[1].first->value();
               v[2] = b[2].first->value();
            }
         };

         template <typename T_>
         struct evaluate_branches <T_,2>
         {
            static inline void execute(T_ (&v)[2], const branch_t (&b)[2])
            {
               v[0] = b[0].first->value();
               v[1] = b[1].first->value();
            }
         };

         template <typename T_>
         struct evaluate_branches <T_,1>
         {
            static inline void execute(T_ (&v)[1], const branch_t (&b)[1])
            {
               v[0] = b[0].first->value();
            }
         };

         template <typename T_, std::size_t ParamCount>
         struct invoke { static inline T execute(ifunction*, branch_t (&)[ParamCount]) { return std::numeric_limits<T_>::quiet_NaN(); } };

         template <typename T_>
         struct invoke<T_,20>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[20])
            { return f(v[0],v[1],v[2],v[3],v[4],v[5],v[6],v[7],v[8],v[9],v[10],v[11],v[12],v[13],v[14],v[15],v[16],v[17],v[18],v[19]); }
         };

         template <typename T_>
         struct invoke<T_,19>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[19])
            { return f(v[0],v[1],v[2],v[3],v[4],v[5],v[6],v[7],v[8],v[9],v[10],v[11],v[12],v[13],v[14],v[15],v[16],v[17],v[18]); }
         };

         template <typename T_>
         struct invoke<T_,18>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[18])
            { return f(v[0],v[1],v[2],v[3],v[4],v[5],v[6],v[7],v[8],v[9],v[10],v[11],v[12],v[13],v[14],v[15],v[16],v[17]); }
         };

         template <typename T_>
         struct invoke<T_,17>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[17])
            { return f(v[0],v[1],v[2],v[3],v[4],v[5],v[6],v[7],v[8],v[9],v[10],v[11],v[12],v[13],v[14],v[15],v[16]); }
         };

         template <typename T_>
         struct invoke<T_,16>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[16])
            { return f(v[0],v[1],v[2],v[3],v[4],v[5],v[6],v[7],v[8],v[9],v[10],v[11],v[12],v[13],v[14],v[15]); }
         };

         template <typename T_>
         struct invoke<T_,15>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[15])
            { return f(v[0],v[1],v[2],v[3],v[4],v[5],v[6],v[7],v[8],v[9],v[10],v[11],v[12],v[13],v[14]); }
         };

         template <typename T_>
         struct invoke<T_,14>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[14])
            { return f(v[0],v[1],v[2],v[3],v[4],v[5],v[6],v[7],v[8],v[9],v[10],v[11],v[12],v[13]); }
         };

         template <typename T_>
         struct invoke<T_,13>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[13])
            { return f(v[0],v[1],v[2],v[3],v[4],v[5],v[6],v[7],v[8],v[9],v[10],v[11],v[12]); }
         };

         template <typename T_>
         struct invoke<T_,12>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[12])
            { return f(v[0],v[1],v[2],v[3],v[4],v[5],v[6],v[7],v[8],v[9],v[10],v[11]); }
         };

         template <typename T_>
         struct invoke<T_,11>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[11])
            { return f(v[0],v[1],v[2],v[3],v[4],v[5],v[6],v[7],v[8],v[9],v[10]); }
         };

         template <typename T_>
         struct invoke<T_,10>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[10])
            { return f(v[0],v[1],v[2],v[3],v[4],v[5],v[6],v[7],v[8],v[9]); }
         };

         template <typename T_>
         struct invoke<T_,9>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[9])
            { return f(v[0],v[1],v[2],v[3],v[4],v[5],v[6],v[7],v[8]); }
         };

         template <typename T_>
         struct invoke<T_,8>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[8])
            { return f(v[0],v[1],v[2],v[3],v[4],v[5],v[6],v[7]); }
         };

         template <typename T_>
         struct invoke<T_, 7>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[ 7])
            { return f(v[0],v[1],v[2],v[3],v[4],v[5],v[6]); } };

         template <typename T_>
         struct invoke<T_,6>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[6])
            { return f(v[0],v[1],v[2],v[3],v[4],v[5]); }
         };

         template <typename T_>
         struct invoke<T_,5>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[5])
            { return f(v[0],v[1],v[2],v[3],v[4]); }
         };

         template <typename T_>
         struct invoke<T_,4>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[4])
            { return f(v[0],v[1],v[2],v[3]); }
         };

         template <typename T_>
         struct invoke<T_,3>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[3])
            { return f(v[0],v[1],v[2]); }
         };

         template <typename T_>
         struct invoke<T_,2>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[2])
            { return f(v[0],v[1]); }
         };

         template <typename T_>
         struct invoke<T_,1>
         {
            static inline T_ execute(ifunction& f, T_ (&v)[1])
            { return f(v[0]); }
         };

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_function;
         }

      private:

         ifunction* function_;
         std::size_t parameter_count_;
         branch_t branch_[N];
      };

      template <typename T, typename IFunction>
      class function_N_node<T,IFunction,0> : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef IFunction ifunction;

         function_N_node(ifunction* func)
         : function_((0 == func->param_count) ? func : reinterpret_cast<ifunction*>(0))
         {}

         inline bool operator <(const function_N_node<T,IFunction,0>& fn) const
         {
            return this < (&fn);
         }

         inline T value() const
         {
            if (0 == function_)
               return std::numeric_limits<T>::quiet_NaN();
            else
               return (*function_)();
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_function;
         }

      private:

         ifunction* function_;
         std::size_t parameter_count_;
      };

      #define exprtk_def_unary_op(OpName) \
      template <typename T> \
      struct OpName##_op \
      { \
         static inline T process(const T& v) { return numeric:: OpName (v); } \
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_##OpName; } \
         static inline details::operator_type operation() { return details::e_##OpName; } \
      };

      exprtk_def_unary_op(abs  )
      exprtk_def_unary_op(acos )
      exprtk_def_unary_op(asin )
      exprtk_def_unary_op(atan )
      exprtk_def_unary_op(ceil )
      exprtk_def_unary_op(cos  )
      exprtk_def_unary_op(cosh )
      exprtk_def_unary_op(exp  )
      exprtk_def_unary_op(floor)
      exprtk_def_unary_op(log  )
      exprtk_def_unary_op(log10)
      exprtk_def_unary_op(neg  )
      exprtk_def_unary_op(pos  )
      exprtk_def_unary_op(round)
      exprtk_def_unary_op(sin  )
      exprtk_def_unary_op(sinh )
      exprtk_def_unary_op(sqrt )
      exprtk_def_unary_op(tan  )
      exprtk_def_unary_op(tanh )
      exprtk_def_unary_op(cot  )
      exprtk_def_unary_op(sec  )
      exprtk_def_unary_op(csc  )
      exprtk_def_unary_op(r2d  )
      exprtk_def_unary_op(d2r  )
      exprtk_def_unary_op(d2g  )
      exprtk_def_unary_op(g2d  )
      exprtk_def_unary_op(notl )
      exprtk_def_unary_op(sgn  )
      exprtk_def_unary_op(erf  )
      exprtk_def_unary_op(erfc )
      #undef exprtk_def_unary_op

      template <typename T>
      struct add_op
      {
         static inline T process(const T& t1, const T& t2) { return t1 + t2; }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_add; }
         static inline details::operator_type operation() { return details::e_add; }
      };

      template <typename T>
      struct mul_op
      {
         static inline T process(const T& t1, const T& t2) { return t1 * t2; }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_mul; }
         static inline details::operator_type operation() { return details::e_mul; }
      };

      template <typename T>
      struct sub_op
      {
         static inline T process(const T& t1, const T& t2) { return t1 - t2; }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_sub; }
         static inline details::operator_type operation() { return details::e_sub; }
      };

      template <typename T>
      struct div_op
      {
         static inline T process(const T& t1, const T& t2) { return t1 / t2; }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_div; }
         static inline details::operator_type operation() { return details::e_div; }
      };

      template <typename T>
      struct mod_op
      {
         static inline T process(const T& t1, const T& t2) { return numeric::modulus<T>(t1,t2); }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_mod; }
         static inline details::operator_type operation() { return details::e_mod; }
      };

      template <typename T>
      struct pow_op
      {
         static inline T process(const T& t1, const T& t2) { return numeric::pow<T>(t1,t2); }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_pow; }
         static inline details::operator_type operation() { return details::e_pow; }
      };

      template <typename T>
      struct lt_op
      {
         static inline T process(const T& t1, const T& t2) { return ((t1 < t2) ? T(1) : T(0)); }
         static inline T process(const std::string& t1, const std::string& t2) { return ((t1 < t2) ? T(1) : T(0)); }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_lt; }
         static inline details::operator_type operation() { return details::e_lt; }
      };

      template <typename T>
      struct lte_op
      {
         static inline T process(const T& t1, const T& t2) { return ((t1 <= t2) ? T(1) : T(0)); }
         static inline T process(const std::string& t1, const std::string& t2) { return ((t1 <= t2) ? T(1) : T(0)); }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_lte; }
         static inline details::operator_type operation() { return details::e_lte; }
      };

      template <typename T>
      struct gt_op
      {
         static inline T process(const T& t1, const T& t2) { return ((t1 > t2) ? T(1) : T(0)); }
         static inline T process(const std::string& t1, const std::string& t2) { return ((t1 > t2) ? T(1) : T(0)); }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_gt; }
         static inline details::operator_type operation() { return details::e_gt; }
      };

      template <typename T>
      struct gte_op
      {
         static inline T process(const T& t1, const T& t2) { return ((t1 >= t2) ? T(1) : T(0)); }
         static inline T process(const std::string& t1, const std::string& t2) { return ((t1 >= t2) ? T(1) : T(0)); }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_gte; }
         static inline details::operator_type operation() { return details::e_gte; }
      };

      template <typename T>
      struct eq_op
      {
         static inline T process(const T& t1, const T& t2) { return ((t1 == t2) ? T(1) : T(0)); }
         static inline T process(const std::string& t1, const std::string& t2) { return ((t1 == t2) ? T(1) : T(0)); }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_eq; }
         static inline details::operator_type operation() { return details::e_eq; }
      };

      template <typename T>
      struct ne_op
      {
         static inline T process(const T& t1, const T& t2) { return ((t1 != t2) ? T(1) : T(0)); }
         static inline T process(const std::string& t1, const std::string& t2) { return ((t1 != t2) ? T(1) : T(0)); }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_ne; }
         static inline details::operator_type operation() { return details::e_ne; }
      };

      template <typename T>
      struct and_op
      {
         static inline T process(const T& t1, const T& t2) { return ((t1 != T(0)) && (t2 != T(0))) ? T(1) : T(0); }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_and; }
         static inline details::operator_type operation() { return details::e_and; }
      };

      template <typename T>
      struct nand_op
      {
         static inline T process(const T& t1, const T& t2) { return ((t1 != T(0)) && (t2 != T(0))) ? T(0) : T(1); }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_nand; }
         static inline details::operator_type operation() { return details::e_nand; }
      };

      template <typename T>
      struct or_op
      {
         static inline T process(const T& t1, const T& t2) { return ((t1 != T(0)) || (t2 != T(0))) ? T(1) : T(0); }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_or; }
         static inline details::operator_type operation() { return details::e_or; }
      };

      template <typename T>
      struct nor_op
      {
         static inline T process(const T& t1, const T& t2) { return ((t1 != T(0)) || (t2 != T(0))) ? T(0) : T(1); }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_nor; }
         static inline details::operator_type operation() { return details::e_nor; }
      };

      template <typename T>
      struct xor_op
      {
         static inline T process(const T& t1, const T& t2) { return numeric::xor_opr<T>(t1,t2); }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_nor; }
         static inline details::operator_type operation() { return details::e_xor; }
      };

      template <typename T>
      struct in_op
      {
         static inline T process(const T&, const T&) { return std::numeric_limits<T>::quiet_NaN(); }
         static inline T process(const std::string& t1, const std::string& t2) { return ((std::string::npos != t2.find(t1)) ? T(1) : T(0)); }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_in; }
         static inline details::operator_type operation() { return details::e_in; }
      };

      template <typename T>
      struct like_op
      {
         static inline T process(const T&, const T&) { return std::numeric_limits<T>::quiet_NaN(); }
         static inline T process(const std::string& t1, const std::string& t2) { return (details::wc_match(t2,t1) ? T(1) : T(0)); }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_like; }
         static inline details::operator_type operation() { return details::e_like; }
      };

      template <typename T>
      struct ilike_op
      {
         static inline T process(const T&, const T&) { return std::numeric_limits<T>::quiet_NaN(); }
         static inline T process(const std::string& t1, const std::string& t2) { return (details::wc_imatch(t2,t1) ? T(1) : T(0)); }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_ilike; }
         static inline details::operator_type operation() { return details::e_ilike; }
      };

      template <typename T>
      struct inrange_op
      {
         static inline T process(const T& t0, const T& t1, const T& t2) { return ((t0 <= t1) && (t1 <= t2)) ? T(1) : T(0); }
         static inline T process(const std::string& t0, const std::string& t1, const std::string& t2)
         {
            return ((t0 <= t1) && (t1 <= t2)) ? T(1) : T(0);
         }
         static inline typename expression_node<T>::node_type type() { return expression_node<T>::e_inranges; }
         static inline details::operator_type operation() { return details::e_ilike; }
      };

      template <typename T, typename Operation>
      class unary_variable_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef Operation operation_t;

         explicit unary_variable_node(T& v)
         : v_(v)
         {}

         inline T value() const
         {
            return Operation::process(v_);
         }

         inline typename expression_node<T>::node_type type() const
         {
            return Operation::type();
         }

         inline operator_type operation() const
         {
            return Operation::operation();
         }

         inline T& v()
         {
            return v_;
         }

      private:

         unary_variable_node(unary_variable_node<T,Operation>&);
         unary_variable_node<T,Operation>& operator=(unary_variable_node<T,Operation>&);

         T& v_;
      };

      template <typename T, typename Operation>
      class unary_branch_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef Operation operation_t;

         explicit unary_branch_node(expression_ptr branch)
         : branch_(branch),
           branch_deletable_(branch_deletable(branch_))

         {}

        ~unary_branch_node()
         {
            if (branch_ && branch_deletable_)
            {
               delete branch_;
               branch_ = 0;
            }
         }

         inline T value() const
         {
            T v = branch_->value();
            return Operation::process(v);
         }

         inline typename expression_node<T>::node_type type() const
         {
            return Operation::type();
         }

         inline operator_type operation() const
         {
            return Operation::operation();
         }

      private:

         unary_branch_node(unary_branch_node<T,Operation>&);
         unary_branch_node<T,Operation>& operator=(unary_branch_node<T,Operation>&);

         expression_ptr branch_;
         bool           branch_deletable_;
      };

      template <typename T>
      class vov_base_node : public expression_node<T>
      {
      public:

         inline virtual operator_type operation() const
         {
            return details::e_default;
         }
      };

      template <typename T>
      class cov_base_node : public expression_node<T>
      {
      public:

         inline virtual operator_type operation() const
         {
            return details::e_default;
         }
      };

      template <typename T>
      class sos_base_node : public expression_node<T>
      {
      public:

         inline virtual operator_type operation() const
         {
            return details::e_default;
         }
      };

      template <typename T>
      class sosos_base_node : public expression_node<T>
      {
      public:

         inline virtual operator_type operation() const
         {
            return details::e_default;
         }
      };

      template <typename T, typename Operation>
      class vov_node : public vov_base_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef Operation operation_t;

         //variable op variable node
         explicit vov_node(T& v0, T& v1)
         : v0_(v0),
           v1_(v1)
         {}

         inline T value() const
         {
            return Operation::process(v0_,v1_);
         }

         inline typename expression_node<T>::node_type type() const
         {
            return Operation::type();
         }

         inline operator_type operation() const
         {
            return Operation::operation();
         }

         inline T& v0()
         {
            return v0_;
         }

         inline T& v1()
         {
            return v1_;
         }

      protected:

         T& v0_;
         T& v1_;

      private:

         vov_node(vov_node<T,Operation>&);
         vov_node<T,Operation>& operator=(vov_node<T,Operation>&);
      };

      template <typename T, typename Type0, typename Type1, typename Operation>
      class vov_nodex : public vov_base_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef Operation operation_t;

         //variable op variable node
         explicit vov_nodex(Type0 v0, Type1 v1)
         : v0_(v0),
           v1_(v1)
         {}

         inline T value() const
         {
            return Operation::process(v0_,v1_);
         }

         inline typename expression_node<T>::node_type type() const
         {
            return Operation::type();
         }

         inline operator_type operation() const
         {
            return Operation::operation();
         }

         inline Type0 v0()
         {
            return v0_;
         }

         inline Type1 v1()
         {
            return v1_;
         }

      protected:

         Type0 v0_;
         Type1 v1_;
      };

      template <typename T, typename Operation>
      class cov_node : public cov_base_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef Operation operation_t;

         //constant op variable node
         explicit cov_node(const T& c, T& v)
         : c_(c),
           v_(v)
         {}

         inline T value() const
         {
            return Operation::process(c_,v_);
         }

         inline typename expression_node<T>::node_type type() const
         {
            return Operation::type();
         }

         inline operator_type operation() const
         {
            return Operation::operation();
         }

         inline T c()
         {
            return c_;
         }

         inline T& v()
         {
            return v_;
         }

      protected:

         T  c_;
         T& v_;

      private:

         cov_node(const cov_node<T,Operation>&);
         cov_node<T,Operation>& operator=(const cov_node<T,Operation>&);
      };

      template <typename T, typename Operation>
      class voc_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef Operation operation_t;

         //variable op constant node
         explicit voc_node(T& v, const T& c)
         : v_(v),
           c_(c)
         {}

         inline T value() const
         {
            return Operation::process(v_,c_);
         }

         inline typename expression_node<T>::node_type type() const
         {
            return Operation::type();
         }

      protected:

         T& v_;
         T  c_;

      private:

         voc_node(const voc_node<T,Operation>&);
         voc_node<T,Operation>& operator=(const voc_node<T,Operation>&);
      };

      template <typename T, typename Operation1, typename Operation2>
      class vovov1_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef std::pair<expression_ptr,bool> branch_t;

         //variable0 op1 (variable1 op2 variable2) node
         explicit vovov1_node(T& v0, vov_node<T,Operation2>& vn)
         : v0_(v0),
           v1_(vn.v0()),
           v2_(vn.v1())
         {}

         inline T value() const
         {
            return Operation1::process(v0_,Operation2::process(v1_,v2_));
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_none;
         }

         inline typename expression_node<T>::node_type type1() const
         {
            return Operation1::type();
         }

         inline typename expression_node<T>::node_type type2() const
         {
            return Operation2::type();
         }

      protected:

         T& v0_;
         T& v1_;
         T& v2_;

      private:

         vovov1_node(const vovov1_node<T,Operation1,Operation2>&);
         vovov1_node<T,Operation1,Operation2>& operator=(const vovov1_node<T,Operation1,Operation2>&);
      };

      template <typename T, typename Operation1, typename Operation2>
      class vovov2_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef std::pair<expression_ptr,bool> branch_t;

         //(variable0 op1 variable1) op2 variable2 node
         explicit vovov2_node(vov_node<T,Operation1>& vn, T& v2)
         : v0_(vn.v0()),
           v1_(vn.v1()),
           v2_(v2)
         {}

         inline T value() const
         {
            return Operation2::process(Operation1::process(v0_,v1_),v2_);
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_none;
         }

         inline typename expression_node<T>::node_type type1() const
         {
            return Operation1::type();
         }

         inline typename expression_node<T>::node_type type2() const
         {
            return Operation2::type();
         }

      protected:

         T& v0_;
         T& v1_;
         T& v2_;

      private:

         vovov2_node(const vovov2_node<T,Operation1,Operation2>&);
         vovov2_node<T,Operation1,Operation2>& operator=(const vovov2_node<T,Operation1,Operation2>&);
      };

      template <typename T, typename Operation1, typename Operation2>
      class covov1_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef std::pair<expression_ptr,bool> branch_t;

         //constant op1 (variable0 op2 variable1) node
         explicit covov1_node(const T& c, vov_node<T,Operation2>& vn)
         : c_(c),
           v0_(vn.v0()),
           v1_(vn.v1())
         {}

         inline T value() const
         {
            return Operation1::process(c_,Operation2::process(v0_,v1_));
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_none;
         }

         inline typename expression_node<T>::node_type type1() const
         {
            return Operation1::type();
         }

         inline typename expression_node<T>::node_type type2() const
         {
            return Operation2::type();
         }

      protected:

         T   c_;
         T& v0_;
         T& v1_;

      private:

         covov1_node(const covov1_node<T,Operation1,Operation2>&);
         covov1_node<T,Operation1,Operation2>& operator=(const covov1_node<T,Operation1,Operation2>&);
      };

      template <typename T, typename Operation1, typename Operation2>
      class covov2_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef std::pair<expression_ptr,bool> branch_t;

         //(constant op1 variable0) op2 variable1 node
         explicit covov2_node(cov_node<T,Operation1>& cvn, T& v1)
         : c_(cvn.c()),
           v0_(cvn.v()),
           v1_(v1)
         {}

         inline T value() const
         {
            return Operation2::process(Operation1::process(c_,v0_),v1_);
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_none;
         }

         inline typename expression_node<T>::node_type type1() const
         {
            return Operation1::type();
         }

         inline typename expression_node<T>::node_type type2() const
         {
            return Operation2::type();
         }

      protected:

         T   c_;
         T& v0_;
         T& v1_;

      private:

         covov2_node(covov2_node<T,Operation1,Operation2>&);
         covov2_node<T,Operation1,Operation2>& operator=(covov2_node<T,Operation1,Operation2>&);
      };

      template <typename T, typename Operation1, typename Operation2, typename Operation3>
      class vovovov_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef std::pair<expression_ptr,bool> branch_t;

         //(variable0 op1 variable1) op2 (variable2 op3 variable3) node
         explicit vovovov_node(vov_node<T,Operation1>& vn0, vov_node<T,Operation3>& vn1)
         : v0_(vn0.v0()),
           v1_(vn0.v1()),
           v2_(vn1.v0()),
           v3_(vn1.v1())
         {}

         inline T value() const
         {
            return Operation2::process(Operation1::process(v0_,v1_),Operation3::process(v2_,v3_));
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_none;
         }

         inline typename expression_node<T>::node_type type1() const
         {
            return Operation1::type();
         }

         inline typename expression_node<T>::node_type type2() const
         {
            return Operation2::type();
         }

      protected:

         T& v0_;
         T& v1_;
         T& v2_;
         T& v3_;

      private:

         vovovov_node(vovovov_node<T,Operation1,Operation2,Operation3>&);
         vovovov_node<T,Operation1,Operation2,Operation3>& operator=(const vovovov_node<T,Operation1,Operation2,Operation3>&);
      };

      #ifndef exprtk_disable_string_capabilities
      template <typename T, typename SType0, typename SType1, typename Operation>
      class sos_node : public sos_base_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef Operation operation_t;

         //variable op variable node
         explicit sos_node(SType0 s0, SType1 s1)
         : s0_(s0),
           s1_(s1)
         {}

         inline T value() const
         {
            return Operation::process(s0_,s1_);
         }

         inline typename expression_node<T>::node_type type() const
         {
            return Operation::type();
         }

         inline operator_type operation() const
         {
            return Operation::operation();
         }

         inline std::string& s0()
         {
            return s0_;
         }

         inline std::string& s1()
         {
            return s1_;
         }

      protected:

         SType0 s0_;
         SType1 s1_;

      private:

         sos_node(sos_node<T,SType0,SType1,Operation>&);
         sos_node<T,SType0,SType1,Operation>& operator=(sos_node<T,SType0,SType1,Operation>&);
      };

      template <typename T, typename SType0, typename SType1, typename SType2, typename Operation>
      class sosos_node : public sosos_base_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef Operation operation_t;

         //variable op variable node
         explicit sosos_node(SType0 s0, SType1 s1, SType2 s2)
         : s0_(s0),
           s1_(s1),
           s2_(s2)
         {}

         inline T value() const
         {
            return Operation::process(s0_,s1_,s2_);
         }

         inline typename expression_node<T>::node_type type() const
         {
            return Operation::type();
         }

         inline operator_type operation() const
         {
            return Operation::operation();
         }

         inline std::string& s0()
         {
            return s0_;
         }

         inline std::string& s1()
         {
            return s1_;
         }

         inline std::string& s2()
         {
            return s2_;
         }

      protected:

         SType0 s0_;
         SType1 s1_;
         SType2 s2_;

      private:

         sosos_node(sosos_node<T,SType0,SType1,SType2,Operation>&);
         sosos_node<T,SType0,SType1,SType2,Operation>& operator=(sosos_node<T,SType0,SType1,SType2,Operation>&);
      };
      #endif

      template <typename T, typename PowOp>
      class ipow_node : public expression_node<T>
      {
      public:

         typedef expression_node<T>* expression_ptr;
         typedef PowOp operation_t;

         //variable op constant node
         explicit ipow_node(T& v, const bool not_recipricol = true)
         : v_(v),
           not_recipricol_(not_recipricol)
         {}

         inline T value() const
         {
            if (not_recipricol_)
               return PowOp::result(v_);
            else
               return (T(1.0) / PowOp::result(v_));
         }

         inline typename expression_node<T>::node_type type() const
         {
            return expression_node<T>::e_ipow;
         }

      private:

         ipow_node(const ipow_node<T,PowOp>&);
         ipow_node<T,PowOp>& operator=(const ipow_node<T,PowOp>&);

         T& v_;
         const bool not_recipricol_;
      };

      template <typename T>
      inline bool is_vov_node(const expression_node<T>* node)
      {
         return (0 != dynamic_cast<const vov_base_node<T>*>(node));
      }

      template <typename T>
      inline bool is_cov_node(const expression_node<T>* node)
      {
         return (0 != dynamic_cast<const cov_base_node<T>*>(node));
      }

      template <typename T>
      inline bool is_string_node(const expression_node<T>* node)
      {
         return (expression_node<T>::e_stringvar == node->type());
      }

      template <typename T>
      inline bool is_const_string_node(const expression_node<T>* node)
      {
         return (expression_node<T>::e_stringconst == node->type());
      }

      class node_allocator
      {
      public:

         template <typename ResultNode, typename OpType, typename ExprNode>
         inline expression_node<typename ResultNode::value_type>* allocate(OpType& operation, ExprNode (&branch)[1])
         {
            return allocate<ResultNode>(operation,branch[0]);
         }

         template <typename ResultNode, typename OpType, typename ExprNode>
         inline expression_node<typename ResultNode::value_type>* allocate(OpType& operation, ExprNode (&branch)[2])
         {
            return allocate<ResultNode>(operation,branch[0],branch[1]);
         }

         template <typename ResultNode, typename OpType, typename ExprNode>
         inline expression_node<typename ResultNode::value_type>* allocate(OpType& operation, ExprNode (&branch)[3])
         {
            return allocate<ResultNode>(operation,branch[0],branch[1],branch[2]);
         }

         template <typename ResultNode, typename OpType, typename ExprNode>
         inline expression_node<typename ResultNode::value_type>* allocate(OpType& operation, ExprNode (&branch)[4])
         {
            return allocate<ResultNode>(operation,branch[0],branch[1],branch[2],branch[3]);
         }

         template <typename ResultNode, typename OpType, typename ExprNode>
         inline expression_node<typename ResultNode::value_type>* allocate(OpType& operation, ExprNode (&branch)[5])
         {
            return allocate<ResultNode>(operation,branch[0],branch[1],branch[2],branch[3],branch[4]);
         }

         template <typename ResultNode, typename OpType, typename ExprNode>
         inline expression_node<typename ResultNode::value_type>* allocate(OpType& operation, ExprNode (&branch)[6])
         {
            return allocate<ResultNode>(operation,branch[0],branch[1],branch[2],branch[3],branch[4],branch[5]);
         }

         template <typename node_type, typename T1>
         inline expression_node<typename node_type::value_type>* allocate(T1& t1) const
         {
            return new node_type(t1);
         }

         template <typename node_type, typename T1>
         inline expression_node<typename node_type::value_type>* allocate_c(const T1& t1) const
         {
            return new node_type(t1);
         }

         template <typename node_type,
                   typename T1, typename T2>
         inline expression_node<typename node_type::value_type>* allocate(const T1& t1, const T2& t2) const
         {
            return new node_type(t1,t2);
         }

         template <typename node_type,
                   typename T1, typename T2>
         inline expression_node<typename node_type::value_type>* allocate_cr(const T1& t1, T2& t2) const
         {
            return new node_type(t1,t2);
         }

         template <typename node_type,
                   typename T1, typename T2>
         inline expression_node<typename node_type::value_type>* allocate_rc(T1& t1, const T2& t2) const
         {
            return new node_type(t1,t2);
         }

         template <typename node_type,
                   typename T1, typename T2>
         inline expression_node<typename node_type::value_type>* allocate_rr(T1& t1, T2& t2) const
         {
            return new node_type(t1,t2);
         }

         template <typename node_type,
                   typename T1, typename T2>
         inline expression_node<typename node_type::value_type>* allocate_tt(T1 t1, T2 t2) const
         {
            return new node_type(t1,t2);
         }

         template <typename node_type,
                   typename T1, typename T2, typename T3>
         inline expression_node<typename node_type::value_type>* allocate_rrr(T1& t1, T2& t2, T3& t3) const
         {
            return new node_type(t1,t2,t3);
         }

         template <typename node_type,
                   typename T1, typename T2, typename T3>
         inline expression_node<typename node_type::value_type>* allocate_type(T1 t1, T2 t2, T3 t3) const
         {
            return new node_type(t1,t2,t3);
         }

         template <typename node_type,
                   typename T1, typename T2,
                   typename T3>
         inline expression_node<typename node_type::value_type>* allocate(const T1& t1, const T2& t2,
                                                                          const T3& t3) const
         {
            return new node_type(t1,t2,t3);
         }

         template <typename node_type,
                   typename T1, typename T2,
                   typename T3, typename T4>
         inline expression_node<typename node_type::value_type>* allocate(const T1& t1, const T2& t2,
                                                                          const T3& t3, const T4& t4) const
         {
            return new node_type(t1,t2,t3,t4);
         }

         template <typename node_type,
                   typename T1, typename T2,
                   typename T3, typename T4, typename T5>
         inline expression_node<typename node_type::value_type>* allocate(const T1& t1, const T2& t2,
                                                                          const T3& t3, const T4& t4,
                                                                          const T5& t5) const
         {
            return new node_type(t1,t2,t3,t4,t5);
         }

         template <typename node_type,
                   typename T1, typename T2,
                   typename T3, typename T4, typename T5, typename T6>
         inline expression_node<typename node_type::value_type>* allocate(const T1& t1, const T2& t2,
                                                                          const T3& t3, const T4& t4,
                                                                          const T5& t5, const T6& t6) const
         {
            return new node_type(t1,t2,t3,t4,t5,t6);
         }

         template <typename node_type,
                   typename T1, typename T2,
                   typename T3, typename T4,
                   typename T5, typename T6, typename T7>
         inline expression_node<typename node_type::value_type>* allocate(const T1& t1, const T2& t2,
                                                                          const T3& t3, const T4& t4,
                                                                          const T5& t5, const T6& t6,
                                                                          const T7& t7) const
         {
            return new node_type(t1,t2,t3,t4,t5,t6,t7);
         }

         template <typename node_type,
                   typename T1, typename T2,
                   typename T3, typename T4,
                   typename T5, typename T6,
                   typename T7, typename T8>
         inline expression_node<typename node_type::value_type>* allocate(const T1& t1, const T2& t2,
                                                                          const T3& t3, const T4& t4,
                                                                          const T5& t5, const T6& t6,
                                                                          const T7& t7, const T8& t8) const
         {
            return new node_type(t1,t2,t3,t4,t5,t6,t7,t8);
         }

         template <typename node_type,
                   typename T1, typename T2,
                   typename T3, typename T4,
                   typename T5, typename T6,
                   typename T7, typename T8, typename T9>
         inline expression_node<typename node_type::value_type>* allocate(const T1& t1, const T2& t2,
                                                                          const T3& t3, const T4& t4,
                                                                          const T5& t5, const T6& t6,
                                                                          const T7& t7, const T8& t8,
                                                                          const T9& t9) const
         {
            return new node_type(t1,t2,t3,t4,t5,t6,t7,t8,t9);
         }

         template <typename node_type,
                   typename T1, typename T2,
                   typename T3, typename T4,
                   typename T5, typename T6,
                   typename T7, typename T8,
                   typename T9, typename T10>
         inline expression_node<typename node_type::value_type>* allocate(const T1& t1, const  T2&  t2,
                                                                          const T3& t3, const  T4&  t4,
                                                                          const T5& t5, const  T6&  t6,
                                                                          const T7& t7, const  T8&  t8,
                                                                          const T9& t9, const T10& t10) const
         {
            return new node_type(t1,t2,t3,t4,t5,t6,t7,t8,t9,t10);
         }

         template <typename T>
         void inline free(expression_node<T>*& e) const
         {
            delete e;
            e = 0;
         }
      };

      struct operation_t
      {
         operation_t(const std::string& n, const operator_type t, const unsigned int& np)
         : name(n),
           type(t),
           num_params(np)
         {}

         std::string name;
         operator_type type;
         unsigned int num_params;
      };

      static const operation_t operation_list[] =
                                 {
                                    operation_t(      "abs" , e_abs    , 1),
                                    operation_t(     "acos" , e_acos   , 1),
                                    operation_t(     "asin" , e_asin   , 1),
                                    operation_t(     "atan" , e_atan   , 1),
                                    operation_t(     "ceil" , e_ceil   , 1),
                                    operation_t(      "cos" , e_cos    , 1),
                                    operation_t(     "cosh" , e_cosh   , 1),
                                    operation_t(      "exp" , e_exp    , 1),
                                    operation_t(    "floor" , e_floor  , 1),
                                    operation_t(      "log" , e_log    , 1),
                                    operation_t(    "log10" , e_log10  , 1),
                                    operation_t(    "round" , e_round  , 1),
                                    operation_t(      "sin" , e_sin    , 1),
                                    operation_t(     "sinh" , e_sinh   , 1),
                                    operation_t(      "sec" , e_sec    , 1),
                                    operation_t(      "csc" , e_csc    , 1),
                                    operation_t(     "sqrt" , e_sqrt   , 1),
                                    operation_t(      "tan" , e_tan    , 1),
                                    operation_t(     "tanh" , e_tanh   , 1),
                                    operation_t(      "cot" , e_cot    , 1),
                                    operation_t(  "rad2deg" , e_r2d    , 1),
                                    operation_t(  "deg2rad" , e_d2r    , 1),
                                    operation_t( "deg2grad" , e_d2g    , 1),
                                    operation_t( "grad2deg" , e_g2d    , 1),
                                    operation_t(      "sgn" , e_sgn    , 1),
                                    operation_t(      "not" , e_notl   , 1),
                                    operation_t(      "erf" , e_erf    , 1),
                                    operation_t(     "erfc" , e_erfc   , 1),
                                    operation_t(    "atan2", e_atan2   , 2),
                                    operation_t(      "min", e_min     , 2),
                                    operation_t(      "max", e_max     , 2),
                                    operation_t(      "avg", e_avg     , 2),
                                    operation_t(      "sum", e_sum     , 2),
                                    operation_t(      "mul", e_prod    , 2),
                                    operation_t(      "mod", e_mod     , 2),
                                    operation_t(     "logn", e_logn    , 2),
                                    operation_t(     "root", e_root    , 2),
                                    operation_t(   "roundn", e_roundn  , 2),
                                    operation_t(    "equal", e_equal   , 2),
                                    operation_t("not_equal", e_nequal  , 2),
                                    operation_t(      "hyp", e_hyp     , 2),
                                    operation_t(      "shr", e_shr     , 2),
                                    operation_t(      "shl", e_shl     , 2),
                                    operation_t(    "clamp", e_clamp   , 3),
                                    operation_t(  "inrange", e_inrange , 3),
                                    operation_t(      "min", e_min     , 3),
                                    operation_t(      "max", e_max     , 3),
                                    operation_t(      "avg", e_avg     , 3),
                                    operation_t(      "sum", e_sum     , 3),
                                    operation_t(      "mul", e_prod    , 3),
                                    operation_t(      "min", e_min     , 4),
                                    operation_t(      "max", e_max     , 4),
                                    operation_t(      "avg", e_avg     , 4),
                                    operation_t(      "sum", e_sum     , 4),
                                    operation_t(      "mul", e_prod    , 4),
                                    operation_t(      "min", e_min     , 5),
                                    operation_t(      "max", e_max     , 5),
                                    operation_t(      "avg", e_avg     , 5),
                                    operation_t(      "sum", e_sum     , 5),
                                    operation_t(      "mul", e_prod    , 5),
                                    operation_t(      "min", e_min     , 6),
                                    operation_t(      "max", e_max     , 6),
                                    operation_t(      "avg", e_avg     , 6),
                                    operation_t(      "sum", e_sum     , 6),
                                    operation_t(      "mul", e_prod    , 6),
                                 };

      static const std::size_t operation_list_size = sizeof(operation_list) / sizeof(operation_t);

   } // namespace details

   template <typename T>
   class ifunction
   {
   public:

      explicit ifunction(const std::size_t& pc)
      : param_count(pc)
      {}

      virtual ~ifunction()
      {}

      std::size_t param_count;

      inline virtual T operator()()
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&,const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&, const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&, const T&, const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&,
                                  const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&,
                                  const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&,
                                  const T&, const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&,
                                  const T&, const T&, const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&,
                                  const T&, const T&, const T&, const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&,
                                  const T&, const T&, const T&, const T&, const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&,
                                  const T&, const T&, const T&, const T&, const T&, const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&,
                                  const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&,
                                  const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&,
                                  const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

   };

   template <typename T>
   class symbol_table
   {
   private:

      struct ilesscompare
      {
         inline bool operator()(const std::string& s1, const std::string& s2) const
         {
            const std::size_t length = std::min(s1.size(),s2.size());
            for (std::size_t i = 0; i < length;  ++i)
            {
               if (std::tolower(s1[i]) > std::tolower(s2[i]))
                  return false;
               else if (std::tolower(s1[i]) < std::tolower(s2[i]))
                  return true;
            }
            return s1.size() < s2.size();
         }
      };

      template <typename Type, typename RawType>
      struct type_store
      {
         typedef typename details::variable_node<T>  variable_node_t;
         typedef ifunction<T>                        ifunction_t;
         #ifndef exprtk_disable_string_capabilities
         typedef typename details::stringvar_node<T> stringvar_node_t;
         #endif

         typedef Type type_t;
         typedef type_t* type_ptr;
         typedef std::pair<bool,type_ptr> type_pair_t;
         typedef std::map<std::string,type_pair_t,ilesscompare> type_map_t;
         typedef typename type_map_t::iterator tm_itr_t;
         typedef typename type_map_t::const_iterator tm_const_itr_t;

         enum { lut_size = 256 };

         type_pair_t short_type_lut[lut_size];
         type_map_t  map;
         std::size_t size;

         type_store()
         : size(0)
         {}

         inline bool symbol_exists(const std::string& symbol_name) const
         {
            if ((1 == symbol_name.size()) && short_type_lut[static_cast<std::size_t>(symbol_name[0])].second)
               return true;
            else if (map.end() != map.find(symbol_name))
               return true;
            else
               return false;
         }

         inline bool is_constant(const std::string& symbol_name) const
         {
            if (1 == symbol_name.size() && short_type_lut[static_cast<std::size_t>(symbol_name[0])].first)
               return true;
            else
            {
               tm_const_itr_t itr = map.find(symbol_name);
               if (map.end() == itr)
                  return false;
               else
                  return (*itr).second.first;
            }
         }

         inline bool add(const std::string& symbol_name, RawType& t, const bool is_constant = false)
         {
            struct tie
            {
               static inline std::pair<bool,variable_node_t*> make(T& t,const bool is_constant = false)
               {
                  return std::make_pair(is_constant,new variable_node_t(t));
               }

               #ifndef exprtk_disable_string_capabilities
               static inline std::pair<bool,stringvar_node_t*> make(std::string& t,const bool is_constant = false)
               {
                  return std::make_pair(is_constant,new stringvar_node_t(t));
               }
               #endif

               static inline std::pair<bool,function_t*> make(function_t& t, const bool is_constant = false)
               {
                  return std::make_pair(is_constant,&t);
               }
            };

            if (1 == symbol_name.size())
            {
               short_type_lut[static_cast<std::size_t>(symbol_name[0])] = tie::make(t,is_constant);
               ++size;
            }
            else
            {
               for (std::size_t i = 0; i < details::reserved_symbols_size; ++i)
               {
                  if (details::imatch(symbol_name,details::reserved_symbols[i]))
                  {
                     return false;
                  }
               }
               tm_itr_t itr = map.find(symbol_name);
               if (map.end() == itr)
               {
                  map[symbol_name] = tie::make(t,is_constant);
                  ++size;
               }
            }
            return true;
         }

         inline type_ptr get(const std::string& symbol_name)
         {
            if (1 == symbol_name.size())
            {
               type_pair_t& tp = short_type_lut[static_cast<std::size_t>(symbol_name[0])];
               if (tp.second)
                  return tp.second;
               else
                  return reinterpret_cast<type_ptr>(0);
            }
            else
            {
               tm_const_itr_t itr = map.find(symbol_name);
               if (map.end() == itr)
                  return reinterpret_cast<type_ptr>(0);
               else
                  return itr->second.second;
            }
         }

         inline bool remove(const std::string& symbol_name)
         {
            if (1 == symbol_name.size())
            {
               type_pair_t& tp = short_type_lut[static_cast<std::size_t>(symbol_name[0])];
               if (0 == tp.second)
                  return false;
               struct deleter
               {
                  static inline void process(std::pair<bool,variable_node_t*>& n)  { delete n.second; }
                  #ifndef exprtk_disable_string_capabilities
                  static inline void process(std::pair<bool,stringvar_node_t*>& n) { delete n.second; }
                  #endif
                  static inline void process(std::pair<bool,function_t*>&)         {                  }
               };
               deleter::process(tp);
               tp.first = false;
               tp.second = 0;
               --size;
               return true;
            }
            else
            {
               tm_itr_t itr = map.find(symbol_name);
               if (map.end() != itr)
               {
                  struct deleter
                  {
                     static inline void process(std::pair<bool,variable_node_t*>& n)  { delete n.second; }
                     #ifndef exprtk_disable_string_capabilities
                     static inline void process(std::pair<bool,stringvar_node_t*>& n) { delete n.second; }
                     #endif
                     static inline void process(std::pair<bool,function_t*>&)         {                  }
                  };
                  deleter::process((*itr).second);
                  map.erase(itr);
                  --size;
                  return true;
               }
               else
                  return false;
            }
         }

         inline RawType& type_ref(const std::string& symbol_name)
         {
            struct init_type
            {
               static inline double set(long double)      { return (0.0);           }
               static inline float  set(float)            { return (0.0f);          }
               static inline std::string set(std::string) { return std::string(""); }
            };
            static RawType null_type = init_type::set(RawType());
            if (1 == symbol_name.size())
            {
               type_pair_t& tp = short_type_lut[static_cast<std::size_t>(symbol_name[0])];
               if (tp.second)
                  return tp->second.ref();
               else
                  return null_type;
            }
            else
            {
               tm_const_itr_t itr = map.find(symbol_name);
               if (map.end() == itr)
                  return null_type;
               else
                  return itr->second.second->ref();
            }
         }

         inline void clear()
         {
            for (std::size_t i = 0; i < lut_size; ++i)
            {
               if (short_type_lut[i].second)
               {
                  delete (short_type_lut[i]).second;
                  short_type_lut[i].first = false;
                  short_type_lut[i].second = reinterpret_cast<type_ptr>(0);
               }
            }
            if (!map.empty())
            {
               tm_itr_t itr = map.begin();
               tm_itr_t end = map.end();
               while (end != itr)
               {
                  struct deleter
                  {
                     static inline void process(std::pair<bool,variable_node_t*>& n)  { delete n.second; }
                     static inline void process(std::pair<bool,function_t*>&)         {                  }
                     #ifndef exprtk_disable_string_capabilities
                     static inline void process(std::pair<bool,stringvar_node_t*>& n) { delete n.second; }
                     #endif
                  };
                  deleter::process((*itr).second);
                  ++itr;
               }
               map.clear();
            }
         }

         template <typename Allocator,
                   template <typename, typename> class Sequence>
         inline std::size_t get_list(Sequence<std::pair<std::string,RawType>,Allocator>& list) const
         {
            std::size_t count = 0;
            for (std::size_t i = 0; i < lut_size; ++i)
            {
               const type_pair_t& tp = short_type_lut[static_cast<std::size_t>(i)];
               if (0 != tp.second)
               {
                  list.push_back(std::make_pair(std::string("") + static_cast<char>(i),tp.second->ref()));
                  ++count;
               }
            }
            if (!map.empty())
            {
               tm_const_itr_t itr = map.begin();
               tm_const_itr_t end = map.end();
               while (end != itr)
               {
                  list.push_back(std::make_pair((*itr).first,itr->second.second->ref()));
                  ++itr;
                  ++count;
               }
            }
            return count;
         }

         template <typename Allocator,
                   template <typename, typename> class Sequence>
         inline std::size_t get_list(Sequence<std::string,Allocator>& vlist) const
         {
            std::size_t count = 0;
            for (std::size_t i = 0; i < lut_size; ++i)
            {
               const type_pair_t& tp = short_type_lut[static_cast<std::size_t>(i)];
               if (0 != tp.second)
               {
                  vlist.push_back(std::string("") + static_cast<char>(i));
                  ++count;
               }
            }
            if (!map.empty())
            {
               tm_const_itr_t itr = map.begin();
               tm_const_itr_t end = map.end();
               while (end != itr)
               {
                  vlist.push_back((*itr).first);
                  ++itr;
                  ++count;
               }
            }
            return count;
         }

      };

      typedef typename details::variable_node<T> variable_t;
      typedef variable_t* variable_ptr;
      #ifndef exprtk_disable_string_capabilities
      typedef typename details::stringvar_node<T> stringvar_t;
      typedef stringvar_t* stringvar_ptr;
      #endif
      typedef ifunction<T> function_t;
      typedef function_t* function_ptr;

      static const std::size_t lut_size = 256;

      struct st_holder
      {
         struct st_data
         {
            type_store<typename details::variable_node<T>,T> variable_store;
            #ifndef exprtk_disable_string_capabilities
            type_store<typename details::stringvar_node<T>,std::string> stringvar_store;
            #endif
            type_store<ifunction<T>,ifunction<T> > function_store;

            st_data()
            {
               for (std::size_t i = 0; i < details::reserved_words_size; ++i)
               {
                  reserved_symbol_table_.insert(details::reserved_words[i]);
               }
               for (std::size_t i = 0; i < details::reserved_symbols_size; ++i)
               {
                  reserved_symbol_table_.insert(details::reserved_symbols[i]);
               }
            }

            inline bool is_reserved_symbol(const std::string& symbol) const
            {
               return (reserved_symbol_table_.end() != reserved_symbol_table_.find(symbol));
            }

            std::list<T> local_symbol_list_;
            std::list<std::string> local_stringvar_list_;
            std::set<std::string> reserved_symbol_table_;
         };

         st_holder()
         : ref_count(1),
           data_(new st_data)
         {}

         st_holder(st_data* data)
         : ref_count(1),
           data_(data)
         {}

        ~st_holder()
         {
            if (data_ && (0 == ref_count))
            {
               delete data_;
               data_ = 0;
            }
         }

         std::size_t ref_count;
         st_data* data_;
      };

   public:

      symbol_table()
      : holder_(new st_holder)
      {
         clear();
      }

     ~symbol_table()
      {
         if (holder_)
         {
            if (0 == --holder_->ref_count)
            {
               clear();
               delete holder_;
            }
         }
      }

      symbol_table(const symbol_table<T>& st)
      {
         holder_ = st.holder_;
         holder_->ref_count++;
      }

      symbol_table<T>& operator=(const symbol_table<T>& st)
      {
         if (holder_)
         {
            if (0 == --holder_->ref_count)
            {
               delete holder_;
            }
            holder_ = 0;
         }
         holder_ = st.holder_;
         holder_->ref_count++;
         return *this;
      }

      inline void clear()
      {
         if (!valid()) return;
         local_data().variable_store.clear();
         local_data().function_store.clear();
         #ifndef exprtk_disable_string_capabilities
         local_data().stringvar_store.clear();
         #endif
      }

      inline std::size_t variable_count() const
      {
         if (valid())
            return local_data().variable_store().size;
         else
            return 0;
      }

      #ifndef exprtk_disable_string_capabilities
      inline std::size_t stringvar_count() const
      {
         if (valid())
            return local_data().stringvar_store().size;
         else
            return 0;
      }
      #endif

      inline std::size_t function_count() const
      {
         if (valid())
            return local_data().function_store().size;
         else
            return 0;
      }

      inline variable_ptr get_variable(const std::string& variable_name)
      {
         if (!valid())
            return reinterpret_cast<variable_ptr>(0);
         else if (!valid_symbol(variable_name))
            return reinterpret_cast<variable_ptr>(0);
         else
            return local_data().variable_store.get(variable_name);
      }

      #ifndef exprtk_disable_string_capabilities
      inline stringvar_ptr get_stringvar(const std::string& string_name)
      {
         if (!valid())
            return reinterpret_cast<stringvar_ptr>(0);
         else if (!valid_symbol(string_name))
            return reinterpret_cast<stringvar_ptr>(0);
         else
            return local_data().stringvar_store.get(string_name);
      }
      #endif

      inline function_ptr get_function(const std::string& function_name)
      {
         if (!valid())
            return reinterpret_cast<function_ptr>(0);
         else if (!valid_symbol(function_name))
            return reinterpret_cast<function_ptr>(0);
         else
            return local_data().function_store.get(function_name);
      }

      inline T& variable_ref(const std::string& symbol_name)
      {
         static T null_var = T(0);
         if (!valid())
            return null_var;
         else if (!valid_symbol(symbol_name))
            return null_var;
         else
            return local_data().variable_store.type_ref(symbol_name);
      }

      #ifndef exprtk_disable_string_capabilities
      inline std::string& stringvar_ref(const std::string& symbol_name)
      {
         static std::string null_stringvar;
         if (!valid())
            return null_stringvar;
         else if (!valid_symbol(symbol_name))
            return null_stringvar;
         else
            return local_data().stringvar_store.type_ref(symbol_name);
      }
      #endif

      inline bool is_constant_node(const std::string& symbol_name) const
      {
         if (!valid())
            return false;
         else if (!valid_symbol(symbol_name))
            return false;
         else if (!local_data().variable_store.symbol_exists(symbol_name))
            return false;
         else
            return local_data().variable_store.is_constant(symbol_name);
      }

      #ifndef exprtk_disable_string_capabilities
      inline bool is_constant_string(const std::string& symbol_name) const
      {
         if (!valid())
            return false;
         else if (!valid_symbol(symbol_name))
            return false;
         else if (!local_data().stringvar_store.symbol_exists(symbol_name))
            return false;
         else
            return local_data().stringvar_store.is_constant(symbol_name);
      }
      #endif

      inline bool create_variable(const std::string& variable_name, const T& value = T(0))
      {
         if (!valid())
            return false;
         else if (!valid_symbol(variable_name))
            return false;
         else if (symbol_exists(variable_name))
            return false;
         local_data().local_symbol_list_.push_back(value);
         T& t = local_data().local_symbol_list_.back();
         return add_variable(variable_name,t);
      }

      #ifndef exprtk_disable_string_capabilities
      inline bool create_stringvar(const std::string& stringvar_name, const std::string& value = std::string(""))
      {
         if (!valid())
            return false;
         else if (!valid_symbol(stringvar_name))
            return false;
         else if (symbol_exists(stringvar_name))
            return false;
         local_data().local_stringvar_list_.push_back(value);
         std::string& s = local_data().local_stringvar_list_.back();
         return add_stringvar(stringvar_name,s);
      }
      #endif

      inline bool add_variable(const std::string& variable_name, T& t, const bool is_constant = false)
      {
         if (!valid())
            return false;
         else if (!valid_symbol(variable_name))
            return false;
         else if (symbol_exists(variable_name))
            return false;
         else
            return local_data().variable_store.add(variable_name,t,is_constant);
      }

      inline bool add_constant(const std::string& constant_name, const T& value)
      {
         if (!valid())
            return false;
         else if (!valid_symbol(constant_name))
            return false;
         else if (symbol_exists(constant_name))
            return false;
         local_data().local_symbol_list_.push_back(value);
         T& t = local_data().local_symbol_list_.back();
         return add_variable(constant_name,t,true);
      }

      #ifndef exprtk_disable_string_capabilities
      inline bool add_stringvar(const std::string& stringvar_name, std::string& s, const bool is_constant = false)
      {
         if (!valid())
            return false;
         else if (!valid_symbol(stringvar_name))
            return false;
         else if (symbol_exists(stringvar_name))
            return false;
         else
            return local_data().stringvar_store.add(stringvar_name,s,is_constant);
      }
      #endif

      inline bool add_function(const std::string& function_name, function_t& function)
      {
         if (!valid())
            return false;
         else if (!valid_symbol(function_name))
            return false;
         else if (symbol_exists(function_name))
            return false;
         else
            return local_data().function_store.add(function_name,function);
      }

      inline bool remove_variable(const std::string& variable_name)
      {
         if (!valid())
            return false;
         else
            return local_data().variable_store.remove(variable_name);
      }

      #ifndef exprtk_disable_string_capabilities
      inline bool remove_stringvar(const std::string& string_name)
      {
         if (!valid())
            return false;
         else
            return local_data().stringvar_store.remove(string_name);
      }
      #endif

      inline bool remove_function(const std::string& function_name)
      {
         if (!valid())
            return false;
         else
            return local_data().function_store.remove(function_name);
      }

      inline bool add_constants()
      {
         return add_pi()      &&
                add_epsilon() &&
                add_infinity();
      }

      inline bool add_pi()
      {
         static const T local_pi = T(details::numeric::constant::pi);
         return add_constant("pi",local_pi);
      }

      inline bool add_epsilon()
      {
         static const T local_epsilon = std::numeric_limits<T>::epsilon();
         return add_constant("epsilon",local_epsilon);
      }

      inline bool add_infinity()
      {
         static const T local_infinity = std::numeric_limits<T>::infinity();
         return add_constant("inf",local_infinity);
      }

      template <typename Allocator,
                template <typename, typename> class Sequence>
      inline std::size_t get_variable_list(Sequence<std::pair<std::string,T>,Allocator>& vlist) const
      {
         if (!valid())
            return 0;
         else
            return local_data().variable_store.get_list(vlist);
      }

      template <typename Allocator,
                template <typename, typename> class Sequence>
      inline std::size_t get_variable_list(Sequence<std::string,Allocator>& vlist) const
      {
         if (!valid())
            return 0;
         else
            return local_data().variable_store.get_list(vlist);
      }

      #ifndef exprtk_disable_string_capabilities
      template <typename Allocator,
                template <typename, typename> class Sequence>
      inline std::size_t get_stringvar_list(Sequence<std::pair<std::string,std::string>,Allocator>& svlist) const
      {
         if (!valid())
            return 0;
         else
            return local_data().stringvar_store.get_list(svlist);
      }

      template <typename Allocator,
                template <typename, typename> class Sequence>
      inline std::size_t get_stringvar_list(Sequence<std::string,Allocator>& svlist) const
      {
         if (!valid())
            return 0;
         else
            return local_data().stringvar_store.get_list(svlist);
      }
      #endif

      inline bool symbol_exists(const std::string& symbol_name) const
      {
         /*
            Will return true if symbol_name exists as either a reserved symbol,
            variable, stringvar or function name in any of the type stores.
         */
         if (!valid())
            return false;
         else if (local_data().variable_store.symbol_exists(symbol_name))
            return true;
         #ifndef exprtk_disable_string_capabilities
         else if (local_data().stringvar_store.symbol_exists(symbol_name))
            return true;
         #endif
         else if (local_data().function_store.symbol_exists(symbol_name))
            return true;
         else if (local_data().is_reserved_symbol(symbol_name))
            return true;
         else
            return false;
      }

      inline bool is_variable(const std::string& variable_name) const
      {
         if (!valid())
            return false;
         else
            return local_data().variable_store.symbol_exists(variable_name);
      }

      #ifndef exprtk_disable_string_capabilities
      inline bool is_stringvar(const std::string& stringvar_name) const
      {
         if (!valid())
            return false;
         else
            return local_data().stringvar_store.symbol_exists(stringvar_name);
      }
      #endif

      inline bool is_function(const std::string& function_name) const
      {
         if (!valid())
            return false;
         else
            return local_data().function_store.symbol_exists(function_name);
      }

      inline bool valid() const
      {
         //symbol table sanity check.
         return holder_ && holder_->data_;
      }

   private:

      inline bool valid_symbol(const std::string& symbol) const
      {
         if (symbol.empty())
            return false;
         if (!details::is_letter(symbol[0]))
            return false;
         else if (symbol.size() > 1)
         {
            for (std::size_t i = 1; i < symbol.size(); ++i)
            {
               if (
                   (!details::is_letter(symbol[i])) &&
                   (!details:: is_digit(symbol[i])) &&
                   ('_' != symbol[i])
                  )
                  return false;
            }
         }
         return (!local_data().is_reserved_symbol(symbol));
      }

      inline typename st_holder::st_data& local_data()
      {
         return *(holder_->data_);
      }

      inline const typename st_holder::st_data& local_data() const
      {
         return *(holder_->data_);
      }

      st_holder* holder_;

   };

   template <typename T> class parser;
   template <typename T> class expression_helper;

   template <typename T>
   class expression
   {
   private:

      typedef details::expression_node<T>* expression_ptr;

      struct expression_holder
      {
         expression_holder()
         : ref_count(0),
           expr(0)
         {}

         expression_holder(expression_ptr e)
         : ref_count(1),
           expr(e)
         {}

        ~expression_holder()
         {
            if (expr && !is_variable_node(expr))
            {
               delete expr;
            }
         }

         std::size_t ref_count;
         expression_ptr expr;
      };

   public:

      expression()
      : expression_holder_(0)
      {}

      expression(const expression& e)
      {
         expression_holder_ = e.expression_holder_;
         expression_holder_->ref_count++;
         symbol_table_ = e.symbol_table_;
      }

      expression& operator=(const expression& e)
      {
         if (expression_holder_)
         {
            if (0 == --expression_holder_->ref_count)
            {
               delete expression_holder_;
            }
            expression_holder_ = 0;
         }
         expression_holder_ = e.expression_holder_;
         expression_holder_->ref_count++;
         symbol_table_ = e.symbol_table_;
         return *this;
      }

      inline bool operator!() const
      {
         return ((0 == expression_holder_) || (0 == expression_holder_->expr));
      }

      inline expression& release()
      {
         if (expression_holder_)
         {
            if (0 == --expression_holder_->ref_count)
            {
               delete expression_holder_;
            }
            expression_holder_ = 0;
         }
         return *this;
      }

     ~expression()
      {
         if (expression_holder_)
         {
            if (0 == --expression_holder_->ref_count)
            {
               if (!is_variable_node(expression_holder_->expr))
               {
                  delete expression_holder_;
               }
            }
         }
      }

      inline T value() const
      {
         if (expression_holder_ && expression_holder_->expr)
            return expression_holder_->expr->value();
         else
            return std::numeric_limits<T>::quiet_NaN();
      }

      inline T operator()() const
      {
         return value();
      }

      inline operator T() const
      {
         return value();
      }

      inline operator bool() const
      {
         return (T(0) != value());
      }

      inline void register_symbol_table(symbol_table<T>& st)
      {
         symbol_table_ = st;
      }

      inline const symbol_table<T>& get_symbol_table() const
      {
         return symbol_table_;
      }

      inline symbol_table<T>& get_symbol_table()
      {
         return symbol_table_;
      }

   private:

      inline void set_expression(const expression_ptr expr)
      {
         if (expr)
         {
            if (expression_holder_)
            {
               if (0 == --expression_holder_->ref_count)
               {
                  delete expression_holder_;
               }
            }
            expression_holder_ = new expression_holder(expr);
         }
      }

      expression_holder* expression_holder_;
      symbol_table<T> symbol_table_;

      friend class parser<T>;
      friend class expression_helper<T>;
   };

   template <typename T>
   class expression_helper
   {
   public:

      static inline bool is_head_constant(const expression<T>& expr)
      {
         return details::is_constant_node(expr.expression_holder_->expr);
      }

      static inline bool is_head_variable(const expression<T>& expr)
      {
         return details::is_variable_node(expr.expression_holder_->expr);
      }

      static inline bool is_head_unary(const expression<T>& expr)
      {
         return details::is_unary_node(expr.expression_holder_->expr);
      }

      static inline bool is_head_binary(const expression<T>& expr)
      {
         return details::is_binary_node(expr.expression_holder_->expr);
      }

      static inline bool is_head_function(const expression<T>& expr)
      {
         return details::is_function(expr.expression_holder_->expr);
      }
   };

   template <typename T>
   class parser
   {
   private:

      enum precedence_level
      {
         e_level00,
         e_level01,
         e_level02,
         e_level03,
         e_level04,
         e_level05,
         e_level06,
         e_level07,
         e_level08,
         e_level09,
         e_level10,
         e_level11,
         e_level12,
         e_level13
      };

      typedef ifunction                <T>                        F;
      typedef ifunction                <T>              ifunction_t;
      typedef details::expression_node <T>        expression_node_t;
      typedef details::literal_node    <T>           literal_node_t;
      typedef details::string_literal_node<T> string_literal_node_t;
      typedef details::unary_node      <T>             unary_node_t;
      typedef details::binary_node     <T>            binary_node_t;
      typedef details::trinary_node    <T>           trinary_node_t;
      typedef details::quaternary_node <T>        quaternary_node_t;
      typedef details::quinary_node    <T>           quinary_node_t;
      typedef details::senary_node     <T>            senary_node_t;
      typedef details::conditional_node<T>       conditional_node_t;
      typedef details::while_loop_node <T>        while_loop_node_t;
      typedef details::variable_node   <T>          variable_node_t;
      #ifndef exprtk_disable_string_capabilities
      typedef details::stringvar_node  <T>         stringvar_node_t;
      #endif
      typedef details::assignment_node <T>        assignment_node_t;
      typedef details::token           <T>                  token_t;
      typedef expression_node_t*                expression_node_ptr;

   public:

      enum optimization_level
      {
         e_none   = 0,
         e_level1 = 1,
         e_level2 = 2,
         e_level3 = 4,
         e_all    = 7
      };

      parser()
      : symbol_name_caching_(false)
      {}

      inline bool compile(const std::string& expression_string, expression<T>& expr, const optimization_level& opt_level = e_all)
      {
         if (!validate_expression(expression_string))
         {
            return false;
         }
         error_description_ = "";
         expression_generator_.set_optimization_level(opt_level);
         expression_generator_.set_allocator(node_allocator_);
         if (!lexer_.process(expression_string))
         {
            set_error(lexer_.error());
            return false;
         }
         symbol_table_ = expr.get_symbol_table();
         symbol_name_cache_.clear();
         next_token();
         expression_node_ptr e = parse_expression();
         if ((0 != e) && (token_t::eof == current_token_.type))
         {
            expr.set_expression(e);
            return !(!expr);
         }
         else
         {
            set_error("parser::compile() - Incomplete expression!");
            symbol_name_cache_.clear();
            if (0 != e) delete e;
            return false;
         }
      }

      inline std::string error() const
      {
         return error_description_;
      }

      inline bool& cache_symbols()
      {
         return symbol_name_caching_;
      }

      template <typename Allocator,
                template <typename,typename> class Sequence>
      inline std::size_t expression_symbols(Sequence<std::string,Allocator>& symbols_list)
      {
         if (!symbol_name_caching_)
            return 0;
         if (symbol_name_cache_.empty())
            return 0;
         std::copy(symbol_name_cache_.begin(),
                   symbol_name_cache_.end(),
                   std::back_inserter(symbols_list));
         return symbol_name_cache_.size();
      }

   private:

      inline void store_token()
      {
         lexer_.store();
         store_current_token_ = current_token_;
      }

      inline void restore_token()
      {
         lexer_.restore();
         current_token_ = store_current_token_;
      }

      inline void next_token()
      {
         current_token_ = lexer_.next_token();
      }

      static const precedence_level default_precedence = e_level00;

      struct state_t
      {
         inline void set(const precedence_level& l,
                         const precedence_level& r,
                         const details::operator_type& o)
         {
            left  = l;
            right = r;
            operation = o;
         }

         inline void reset()
         {
            left  = e_level00;
            right = e_level00;
         }

         precedence_level left;
         precedence_level right;
         details::operator_type operation;
      };

      inline expression_node_ptr parse_expression(precedence_level precedence = e_level00)
      {
         expression_node_ptr expr = parse_branch();

         if (0 == expr)
         {
            return expr;
         }

         bool break_loop = false;

         state_t current_state;

         for ( ; ; )
         {
            current_state.reset();
            switch (current_token_.type)
            {
               case token_t::assign : current_state.set(e_level00,e_level00,details::e_assign); break;
               case token_t::lt     : current_state.set(e_level05,e_level06,details::    e_lt); break;
               case token_t::lte    : current_state.set(e_level05,e_level06,details::   e_lte); break;
               case token_t::eq     : current_state.set(e_level05,e_level06,details::    e_eq); break;
               case token_t::ne     : current_state.set(e_level05,e_level06,details::    e_ne); break;
               case token_t::gte    : current_state.set(e_level05,e_level06,details::   e_gte); break;
               case token_t::gt     : current_state.set(e_level05,e_level06,details::    e_gt); break;
               case token_t::add    : current_state.set(e_level07,e_level08,details::   e_add); break;
               case token_t::sub    : current_state.set(e_level07,e_level08,details::   e_sub); break;
               case token_t::div    : current_state.set(e_level10,e_level11,details::   e_div); break;
               case token_t::mul    : current_state.set(e_level10,e_level11,details::   e_mul); break;
               case token_t::mod    : current_state.set(e_level10,e_level11,details::   e_mod); break;
               case token_t::pow    : current_state.set(e_level12,e_level12,details::   e_pow); break;
               default              : if (token_t::symbol == current_token_.type)
                                      {
                                         static const std::string s_and  =    "and";
                                         static const std::string s_nand =   "nand";
                                         static const std::string s_or   =     "or";
                                         static const std::string s_nor  =    "nor";
                                         static const std::string s_xor  =    "xor";
                                         static const std::string s_in   =     "in";
                                         static const std::string s_like =   "like";
                                         static const std::string s_ilike = "ilike";
                                         if (details::imatch(current_token_.value,s_and))
                                         {
                                            current_state.set(e_level01,e_level02,details::e_and);
                                            break;
                                         }
                                         else if (details::imatch(current_token_.value,s_nand))
                                         {
                                            current_state.set(e_level01,e_level02,details::e_nand);
                                            break;
                                         }
                                         else if (details::imatch(current_token_.value,s_or))
                                         {
                                            current_state.set(e_level03,e_level04,details::e_or);
                                            break;
                                         }
                                         else if (details::imatch(current_token_.value,s_nor))
                                         {
                                            current_state.set(e_level03,e_level04,details::e_nor);
                                            break;
                                         }
                                         else if (details::imatch(current_token_.value,s_xor))
                                         {
                                            current_state.set(e_level03,e_level04,details::e_xor);
                                            break;
                                         }
                                         else if (details::imatch(current_token_.value,s_in))
                                         {
                                            current_state.set(e_level03,e_level04,details::e_in);
                                            break;
                                         }
                                         else if (details::imatch(current_token_.value,s_like))
                                         {
                                            current_state.set(e_level03,e_level04,details::e_like);
                                            break;
                                         }
                                         else if (details::imatch(current_token_.value,s_ilike))
                                         {
                                            current_state.set(e_level03,e_level04,details::e_ilike);
                                            break;
                                         }
                                      }
                                      break_loop = true;
            }
            if (break_loop)
               break;
            else if (current_state.left < precedence)
               break;
            next_token();
            expr = expression_generator_(current_state.operation,expr,parse_expression(current_state.right));
            if (0 == expr)
            {
               return expr;
            }
         }
         return expr;
      }

      static inline expression_node_ptr error_node()
      {
         return reinterpret_cast<expression_node_ptr>(0);
      }

      template <typename Type, std::size_t N>
      struct scoped_delete
      {
         typedef Type* ptr_t;

         scoped_delete(parser<T>& pr, ptr_t& p)
         : delete_ptr(true),
           parser_(pr),
           p_(&p)
         {}

         scoped_delete(parser<T>& pr, ptr_t (&p)[N])
         : delete_ptr(true),
           parser_(pr),
           p_(&p[0])
         {}

        ~scoped_delete()
         {
            if (delete_ptr)
            {
               for (std::size_t i = 0; i < N; ++i)
               {
                  if (p_[i] && !is_variable_node(p_[i]))
                  {
                     parser_.node_allocator_.free(p_[i]);
                  }
               }
            }
         }
         bool delete_ptr;
         parser<T>& parser_;
         ptr_t* p_;

      private:

         scoped_delete<Type,N>& operator=(const scoped_delete<Type,N>&);
      };

      template <std::size_t NumberofParameters>
      inline expression_node_ptr parse_function_call(const details::operator_type& opt_type)
      {
         expression_node_ptr branch[NumberofParameters];
         expression_node_ptr result  = 0;
         std::fill_n(branch,NumberofParameters,reinterpret_cast<expression_node_ptr>(0));
         scoped_delete<expression_node_t,NumberofParameters> sd(*this,branch);
         store_token();
         next_token();
         if (!token_is(token_t::lbracket))
         {
            return error_node();
         }
         for (int i = 0; i < static_cast<int>(NumberofParameters); ++i)
         {
            branch[i] = parse_expression();
            if (0 == branch[i])
            {
               return error_node();
            }
            else if (i < static_cast<int>(NumberofParameters - 1))
            {
               if (!token_is(token_t::comma))
               {
                  return error_node();
               }
            }
         }
         if (!token_is(token_t::rbracket))
         {
            return error_node();
         }
         else
            result = expression_generator_(opt_type,branch);
         sd.delete_ptr = false;
         return result;
      }

      template <std::size_t NumberofParameters>
      inline expression_node_ptr parse_function_call(ifunction<T>* function)
      {
         expression_node_ptr branch[NumberofParameters];
         expression_node_ptr result  = 0;
         std::fill_n(branch,NumberofParameters,reinterpret_cast<expression_node_ptr>(0));
         scoped_delete<expression_node_t,NumberofParameters> sd(*this,branch);
         next_token();
         if (!token_is(token_t::lbracket))
         {
            return error_node();
         }
         for (int i = 0; i < static_cast<int>(NumberofParameters); ++i)
         {
            branch[i] = parse_expression();
            if (0 == branch[i])
            {
               return error_node();
            }
            else if (i < static_cast<int>(NumberofParameters - 1))
            {
               if (!token_is(token_t::comma))
               {
                  return error_node();
               }
            }
         }
         if (!token_is(token_t::rbracket))
         {
            return error_node();
         }
         else
            result = expression_generator_.function(function,branch);
         sd.delete_ptr = false;
         return result;
      }

      inline expression_node_ptr parse_conditional_statement()
      {
         //Parse: [if][(][condition][,][consequent][,][alternative][)]
         expression_node_ptr condition   = 0;
         expression_node_ptr consequent  = 0;
         expression_node_ptr alternative = 0;
         next_token();
         if (token_is(token_t::lbracket))
         {
            condition = parse_expression();
            if (0 == condition)
               return error_node();
         }
         else
            return error_node();
         if (token_is(token_t::comma))
         {
            consequent = parse_expression();
            if (0 == consequent)
               return error_node();
         }
         else
            return error_node();
         if (token_is(token_t::comma))
         {
            alternative = parse_expression();
            if (0 == alternative)
               return error_node();
         }
         else
            return error_node();
         if (token_is(token_t::rbracket))
            return expression_generator_.conditional(condition,consequent,alternative);
         else
            return error_node();
      }

      inline expression_node_ptr parse_while_loop()
      {
         //Parse: [while][(][test expr][)][{][expression][}]
         expression_node_ptr condition = 0;
         expression_node_ptr branch = 0;
         next_token();
         if (token_is(token_t::lbracket))
            condition = parse_expression();
         else
            return error_node();
         if (!token_is(token_t::rbracket))
            return error_node();
         if (token_is(token_t::lcrlbracket))
            branch = parse_expression();
         else
            return error_node();
         if (token_is(token_t::rcrlbracket))
            return expression_generator_.while_loop(condition,branch);
         else
            return error_node();
      }

      inline expression_node_ptr parse_special_function(const unsigned int id)
      {
         //Expect: $fDD(expr0,expr1,expr2) or $fDD(expr0,expr1,expr2,expr3)
         const std::size_t sf_3_to_4 = details::e_sf35;
         const details::operator_type opt_type = details::operator_type(id + 1000);
         const std::size_t NumberOfParameters = (id < (sf_3_to_4 - 1000)) ? 3 : 4;
         expression_node_ptr branch3[3];
         expression_node_ptr branch4[4];
         expression_node_ptr* branch = (id < (sf_3_to_4 - 1000)) ? &branch3[0] : &branch4[0];
         expression_node_ptr result  = 0;
         std::fill_n(branch3,3,reinterpret_cast<expression_node_ptr>(0));
         std::fill_n(branch4,4,reinterpret_cast<expression_node_ptr>(0));
         scoped_delete<expression_node_t,3> sd3(*this,branch3);
         scoped_delete<expression_node_t,4> sd4(*this,branch4);
         next_token();
         if (!token_is(token_t::lbracket))
         {
            return error_node();
         }
         for (std::size_t i = 0; i < NumberOfParameters; ++i)
         {
            branch[i] = parse_expression();
            if (0 == branch[i])
            {
               return error_node();
            }
            else if (i < (NumberOfParameters - 1))
            {
               if (!token_is(token_t::comma))
               {
                  return error_node();
               }
            }
         }
         if (!token_is(token_t::rbracket))
            return error_node();
         else
         {
            switch (NumberOfParameters)
            {
               case 3  : result = expression_generator_.special_function(opt_type,branch3); break;
               case 4  : result = expression_generator_.special_function(opt_type,branch4); break;
               default : return error_node();
            }
         }
         sd3.delete_ptr = false;
         sd4.delete_ptr = false;
         return result;
      }

      inline expression_node_ptr parse_symbol()
      {
         std::pair<bool,std::string> match_found_error(false,"");
         if (current_token_.value.size() > 1)
         {
            for (std::size_t i = 0; i < details::operation_list_size; ++i)
            {
               if (details::imatch(details::operation_list[i].name,current_token_.value))
               {
                  store_token();
                  std::string token_value = current_token_.value;
                  expression_node_ptr branch = reinterpret_cast<expression_node_ptr>(0);
                  switch (details::operation_list[i].num_params)
                  {
                     case 1 : branch = parse_function_call<1>(details::operation_list[i].type); break;
                     case 2 : branch = parse_function_call<2>(details::operation_list[i].type); break;
                     case 3 : branch = parse_function_call<3>(details::operation_list[i].type); break;
                     case 4 : branch = parse_function_call<4>(details::operation_list[i].type); break;
                     case 5 : branch = parse_function_call<5>(details::operation_list[i].type); break;
                     case 6 : branch = parse_function_call<6>(details::operation_list[i].type); break;
                  }
                  if (branch)
                  {
                     return branch;
                  }
                  else if (!match_found_error.first)
                  {
                     match_found_error.first = true;
                     match_found_error.second = token_value;
                     set_error("");
                  }
                  restore_token();
               }
            }

            if (match_found_error.first)
            {
               set_error("parser::parse_branch() - invalid argument count for function: " + match_found_error.second);
               return error_node();
            }
         }

         static const std::string symbol_if = "if";
         static const std::string symbol_while = "while";
         if (details::imatch(current_token_.value,symbol_if))
         {
            return parse_conditional_statement();
         }
         else if (details::imatch(current_token_.value,symbol_while))
         {
            return parse_while_loop();
         }
         else if ((current_token_.value.size() == 4) && '$' == current_token_.value[0] && details::imatch('f',current_token_.value[1]))
         {
            unsigned int id = (current_token_.value[2] - '0') * 10 + (current_token_.value[3] - '0');
            if (id <= 99)
               return parse_special_function(id);
            else
            {
               set_error("parser::parse_branch() - invalid special function: " + current_token_.value);
               return error_node();
            }
         }
         else if (symbol_table_.valid())
         {
            const std::string& symbol = current_token_.value;
            //Are we dealing with a variable or a special constant?
            expression_node_ptr variable = symbol_table_.get_variable(symbol);
            if (variable)
            {
               if (symbol_name_caching_)
               {
                  symbol_name_cache_.push_back(symbol);
               }
               if (symbol_table_.is_constant_node(symbol))
               {
                  variable = expression_generator_(variable->value());
               }
               next_token();
               return variable;
            }

            #ifndef exprtk_disable_string_capabilities
            //Are we dealing with a string variable?
            variable = symbol_table_.get_stringvar(symbol);
            if (variable)
            {
               if (symbol_name_caching_)
               {
                  symbol_name_cache_.push_back(symbol);
               }
               if (symbol_table_.is_constant_node(symbol))
               {
                  variable = expression_generator_(dynamic_cast<details::string_literal_node<T>*>(variable)->str());
               }
               next_token();
               return variable;
            }
            #endif

            //Are we dealing with a function?
            ifunction<T>* function = symbol_table_.get_function(symbol);
            if (function)
            {
               expression_node_ptr func_node = reinterpret_cast<expression_node_ptr>(0);
               switch (function->param_count)
               {
                  case  0 : func_node = expression_generator_.function(function); break;
                  case  1 : func_node = parse_function_call< 1>(function); break;
                  case  2 : func_node = parse_function_call< 2>(function); break;
                  case  3 : func_node = parse_function_call< 3>(function); break;
                  case  4 : func_node = parse_function_call< 4>(function); break;
                  case  5 : func_node = parse_function_call< 5>(function); break;
                  case  6 : func_node = parse_function_call< 6>(function); break;
                  case  7 : func_node = parse_function_call< 7>(function); break;
                  case  8 : func_node = parse_function_call< 8>(function); break;
                  case  9 : func_node = parse_function_call< 9>(function); break;
                  case 10 : func_node = parse_function_call<10>(function); break;
                  case 11 : func_node = parse_function_call<11>(function); break;
                  case 12 : func_node = parse_function_call<12>(function); break;
                  case 13 : func_node = parse_function_call<13>(function); break;
                  case 14 : func_node = parse_function_call<14>(function); break;
                  case 15 : func_node = parse_function_call<15>(function); break;
                  case 16 : func_node = parse_function_call<16>(function); break;
                  case 17 : func_node = parse_function_call<17>(function); break;
                  case 18 : func_node = parse_function_call<18>(function); break;
                  case 19 : func_node = parse_function_call<19>(function); break;
                  case 20 : func_node = parse_function_call<20>(function); break;
                  default : {
                              set_error("parser::parse_branch() - invalid number of parameters for function: " + symbol);
                              return expression_node_ptr(0);
                            }
               }
               if (func_node)
                  return func_node;
               else
               {
                  set_error("parser::parse_branch() - failed to generate node for function: " + symbol);
                  return error_node();
               }
            }
            else
            {
               set_error("parser::parse_branch() - undefined variable or function: " + symbol);
               return error_node();
            }
         }
         else
         {
            set_error("parser::parse_branch() - variable or function detected, yet symbol-table is invalid" + current_token_.value);
            return error_node();
         }
      }

      inline expression_node_ptr parse_branch()
      {
         switch (current_token_.type)
         {
            case token_t::number :
                                 {
                                    expression_node_ptr literal_exp = expression_generator_(current_token_.numeric_value);
                                    next_token();
                                    return literal_exp;
                                 }

            case token_t::symbol : return parse_symbol();

            #ifndef exprtk_disable_string_capabilities
            case token_t::string :
                                 {
                                    expression_node_ptr literal_exp = expression_generator_(current_token_.value);
                                    next_token();
                                    return literal_exp;
                                 }
            #endif

            case '(' :
                                 {
                                    next_token();
                                    expression_node_ptr branch = parse_expression();
                                    if (token_is(token_t::rbracket))
                                       return branch;
                                    else
                                       return error_node();
                                 }
            case '[' :
                                 {
                                    next_token();
                                    expression_node_ptr branch = parse_expression();
                                    if (token_is(token_t::rsqrbracket))
                                       return branch;
                                    else
                                       return error_node();
                                 }
            case '{' :
                                 {
                                    next_token();
                                    expression_node_ptr branch = parse_expression();
                                    if (token_is(token_t::rcrlbracket))
                                       return branch;
                                    else
                                       return error_node();
                                 }
            case '-' :
                                 {
                                    next_token();
                                    return expression_generator_(details::e_neg,parse_expression(e_level09));
                                 }
            case '+' :
                                 {
                                    next_token();
                                    return expression_generator_(details::e_pos,parse_expression(e_level09));
                                 }
            case token_t::eof :
                                 {
                                    set_error("parser::parse_branch() - expected a valid branch [1]");
                                    return error_node();
                                 }
            default :
                                 {
                                    set_error("parser::parse_branch() - expected a valid branch [2]");
                                    return error_node();
                                 }
         }
      }

      inline bool token_is(const typename token_t::token_type& ttype)
      {
         if (current_token_.type != ttype)
         {
            if (!((']' == current_token_.type) && (token_t::rbracket == ttype)))
            {
               set_error(std::string("parser::token_is() - expected: ") + static_cast<char>(ttype));
               return false;
            }
         }
         next_token();
         return true;
      }

      template <typename Type>
      class expression_generator
      {
      public:

         typedef details::expression_node<Type>* expression_node_ptr;

         inline void set_optimization_level(const optimization_level& optimization_level)
         {
            optimization_level_ = optimization_level;
         }

         inline void set_allocator(details::node_allocator& na)
         {
            node_allocator_ = &na;
         }

         inline expression_node_ptr operator()(const Type& v) const
         {
            return node_allocator_->allocate<literal_node_t>(v);
         }

         inline expression_node_ptr operator()(const std::string& s) const
         {
            return node_allocator_->allocate<string_literal_node_t>(s);
         }

         inline bool unary_optimizable(const details::operator_type& operation) const
         {
            return (details::e_abs   == operation) || (details::e_acos  == operation) ||
                   (details::e_asin  == operation) || (details::e_atan  == operation) ||
                   (details::e_ceil  == operation) || (details::e_cos   == operation) ||
                   (details::e_cosh  == operation) || (details::e_exp   == operation) ||
                   (details::e_floor == operation) || (details::e_log   == operation) ||
                   (details::e_log10 == operation) || (details::e_neg   == operation) ||
                   (details::e_pos   == operation) || (details::e_round == operation) ||
                   (details::e_sin   == operation) || (details::e_sinh  == operation) ||
                   (details::e_sqrt  == operation) || (details::e_tan   == operation) ||
                   (details::e_tanh  == operation) || (details::e_cot   == operation) ||
                   (details::e_sec   == operation) || (details::e_csc   == operation) ||
                   (details::e_r2d   == operation) || (details::e_d2r   == operation) ||
                   (details::e_d2g   == operation) || (details::e_g2d   == operation) ||
                   (details::e_notl  == operation) || (details::e_sgn   == operation) ||
                   (details::e_erf   == operation) || (details::e_erfc  == operation);
         }

         inline expression_node_ptr operator()(const details::operator_type& operation, expression_node_ptr (&branch)[1])
         {
            if (0 == branch[0])
               return error_node();
            else if (details::is_constant_node(branch[0]))
               return synthesize_expression<unary_node_t,1>(operation,branch);
            else if (unary_optimizable(operation) && details::is_variable_node(branch[0]))
               return synthesize_uv_expression(operation,branch);
            else
               return synthesize_unary_expression(operation,branch);
         }

         #ifndef exprtk_disable_string_capabilities
         inline bool valid_string_operation(const details::operator_type& operation) const
         {
            return (details::e_add   == operation) ||
                   (details::e_lt    == operation) ||
                   (details::e_lte   == operation) ||
                   (details::e_gt    == operation) ||
                   (details::e_gte   == operation) ||
                   (details::e_eq    == operation) ||
                   (details::e_ne    == operation) ||
                   (details::e_in    == operation) ||
                   (details::e_like  == operation) ||
                   (details::e_ilike == operation);
         }
         #else
         inline bool valid_string_operation(const details::operator_type&) const
         {
            return false;
         }
         #endif

         inline bool operation_optimizable(const details::operator_type& operation) const
         {
            return (details::e_add  == operation) ||
                   (details::e_sub  == operation) ||
                   (details::e_mul  == operation) ||
                   (details::e_div  == operation) ||
                   (details::e_mod  == operation) ||
                   (details::e_pow  == operation) ||
                   #ifndef exprtk_disable_extended_operator_optimizations
                   (details::e_lt   == operation) ||
                   (details::e_lte  == operation) ||
                   (details::e_gt   == operation) ||
                   (details::e_gte  == operation) ||
                   (details::e_eq   == operation) ||
                   (details::e_ne   == operation) ||
                   (details::e_and  == operation) ||
                   (details::e_nand == operation) ||
                   (details::e_or   == operation) ||
                   (details::e_nor  == operation) ||
                   (details::e_xor  == operation) ||
                   #endif
                   false;
         }

         inline bool is_level_optimizable(const std::size_t& level = 0) const
         {
            switch (level)
            {
               case 1  : return (e_level1 == (optimization_level_ & e_level1));
               case 2  : return (e_level2 == (optimization_level_ & e_level2)) && is_level_optimizable(1);
               case 3  : return (e_level3 == (optimization_level_ & e_level3)) && is_level_optimizable(2);
               case 0  : return (e_all    == (optimization_level_ &    e_all));
               default : return false;
            }
         }

         inline bool cov_optimizable(const details::operator_type& operation, expression_node_ptr (&branch)[2]) const
         {
            if (!operation_optimizable(operation))
               return false;
            else if (!is_level_optimizable(1))
               return false;
            else
               return (details::is_constant_node(branch[0]) && details::is_variable_node(branch[1]));
         }

         inline bool voc_optimizable(const details::operator_type& operation, expression_node_ptr (&branch)[2]) const
         {
            if (!operation_optimizable(operation))
               return false;
            else if (!is_level_optimizable(1))
               return false;
            else
               return (details::is_variable_node(branch[0]) && details::is_constant_node(branch[1]));
         }

         inline bool vov_optimizable(const details::operator_type& operation, expression_node_ptr (&branch)[2]) const
         {
            if (!operation_optimizable(operation))
               return false;
            else if (!is_level_optimizable(1))
               return false;
            else
               return (details::is_variable_node(branch[0]) && details::is_variable_node(branch[1]));
         }

         inline bool vovov1_optimizable(const details::operator_type& operation, expression_node_ptr (&branch)[2]) const
         {
            if (!operation_optimizable(operation))
               return false;
            else if (!is_level_optimizable(2))
               return false;
            else
               return (details::is_variable_node(branch[0]) && details::is_vov_node(branch[1]));
         }

         inline bool vovov2_optimizable(const details::operator_type& operation, expression_node_ptr (&branch)[2]) const
         {
            if (!operation_optimizable(operation))
               return false;
            else if (!is_level_optimizable(2))
               return false;
            else
               return (details::is_vov_node(branch[0]) && details::is_variable_node(branch[1]));
         }

         inline bool covov1_optimizable(const details::operator_type& operation, expression_node_ptr (&branch)[2]) const
         {
            if (!operation_optimizable(operation))
               return false;
            else if (!is_level_optimizable(2))
               return false;
            else
               return (details::is_constant_node(branch[0]) && details::is_vov_node(branch[1]));
         }

         inline bool covov2_optimizable(const details::operator_type& operation, expression_node_ptr (&branch)[2]) const
         {
            if (!operation_optimizable(operation))
               return false;
            else if (!is_level_optimizable(2))
               return false;
            else
               return (details::is_cov_node(branch[0]) && details::is_variable_node(branch[1]));
         }

         inline bool is_invalid_string_op(const details::operator_type& operation, expression_node_ptr (&branch)[2])
         {
            const bool b0_string = details::is_string_node(branch[0]) || details::is_const_string_node(branch[0]);
            const bool b1_string = details::is_string_node(branch[1]) || details::is_const_string_node(branch[1]);
            if ((b0_string || b1_string) && !(b0_string && b1_string))
               return true;
            if (!valid_string_operation(operation) && b0_string && b1_string)
               return true;
            else
               return false;
         }

         inline bool is_invalid_string_op(const details::operator_type& operation, expression_node_ptr (&branch)[3])
         {
            bool b0_string = details::is_string_node(branch[0]) || details::is_const_string_node(branch[0]);
            bool b1_string = details::is_string_node(branch[1]) || details::is_const_string_node(branch[1]);
            bool b2_string = details::is_string_node(branch[2]) || details::is_const_string_node(branch[2]);
            if ((b0_string || b1_string || b2_string) && !(b0_string && b1_string && b2_string))
               return true;
            if ((details::e_inrange != operation) && b0_string && b1_string && b2_string)
               return true;
            else
               return false;
         }

         inline bool is_string_operation(const details::operator_type& operation, expression_node_ptr (&branch)[2])
         {
            const bool b0_string = details::is_string_node(branch[0]) || details::is_const_string_node(branch[0]);
            const bool b1_string = details::is_string_node(branch[1]) || details::is_const_string_node(branch[1]);
            return (b0_string && b1_string && valid_string_operation(operation));
         }

         inline bool is_string_operation(const details::operator_type& operation, expression_node_ptr (&branch)[3])
         {
            const bool b0_string = details::is_string_node(branch[0]) || details::is_const_string_node(branch[0]);
            const bool b1_string = details::is_string_node(branch[1]) || details::is_const_string_node(branch[1]);
            const bool b2_string = details::is_string_node(branch[2]) || details::is_const_string_node(branch[2]);
            return (b0_string && b1_string && b2_string && (details::e_inrange == operation));
         }

         // Note: Extended Optimisations
         // When using older C++ compilers due to the large number of type instantiations
         // required by the extended optimisations the compiler may crash or not be able
         // to compile this translation unit properly.
         #if defined(_WIN32) || defined(__WIN32__) || defined(WIN32)
            #if (defined(_MSC_VER) && (_MSC_VER <= 1400))
               #ifndef exprtk_disable_extended_optimisations
                  #define exprtk_disable_extended_optimisations
               #endif
            #endif
         #endif

         #ifndef exprtk_disable_extended_optimisations
         inline bool vovovov_optimizable(const details::operator_type& operation, expression_node_ptr (&branch)[2]) const
         {
            if (!operation_optimizable(operation))
               return false;
            else if (!is_level_optimizable(3))
               return false;
            else
               return (details::is_vov_node(branch[0]) && details::is_vov_node(branch[1]));
         }
         #else
         inline bool vovovov_optimizable(const details::operator_type&, expression_node_ptr (&)[2]) const
         {
            return false;
         }
         #endif

         inline expression_node_ptr operator()(const details::operator_type& operation, expression_node_ptr (&branch)[2])
         {
            if ((0 == branch[0]) || (0 == branch[1]))
               return error_node();
            else if (is_invalid_string_op(operation,branch))
               return error_node();
            else if (details::e_assign == operation)
               return synthesize_assignment_expression(operation,branch);
            else if (is_string_operation(operation,branch))
               return synthesize_string_expression(operation,branch);
            else if (cov_optimizable(operation,branch))
               return synthesize_cov_expression(operation,branch);
            else if (voc_optimizable(operation,branch))
               return synthesize_voc_expression(operation,branch);
            else if (vov_optimizable(operation,branch))
               return synthesize_vov_expression(operation,branch);
            else if (vovov1_optimizable(operation,branch))
               return synthesize_vovov1_expression(operation,branch);
            else if (vovov2_optimizable(operation,branch))
               return synthesize_vovov2_expression(operation,branch);
            else if (covov1_optimizable(operation,branch))
               return synthesize_covov1_expression(operation,branch);
            else if (covov2_optimizable(operation,branch))
               return synthesize_covov2_expression(operation,branch);
            else if (vovovov_optimizable(operation,branch))
               return synthesize_vovovov_expression(operation,branch);
            else
               return synthesize_expression<binary_node_t,2>(operation,branch);
         }

         inline expression_node_ptr operator()(const details::operator_type& operation, expression_node_ptr (&branch)[3])
         {
            if ((0 == branch[0]) || (0 == branch[1]) || (0 == branch[2]))
               return error_node();
            else if (is_invalid_string_op(operation,branch))
               return error_node();
            else if (is_string_operation(operation,branch))
               return synthesize_string_expression(operation,branch);
            else
               return synthesize_expression<trinary_node_t,3>(operation,branch);
         }

         inline expression_node_ptr operator()(const details::operator_type& operation, expression_node_ptr (&branch)[4])
         {
            return synthesize_expression<quaternary_node_t,4>(operation,branch);
         }

         inline expression_node_ptr operator()(const details::operator_type& operation, expression_node_ptr (&branch)[5])
         {
            return synthesize_expression<quinary_node_t,5>(operation,branch);
         }

         inline expression_node_ptr operator()(const details::operator_type& operation, expression_node_ptr (&branch)[6])
         {
            return synthesize_expression<senary_node_t,6>(operation,branch);
         }

         inline expression_node_ptr operator()(const details::operator_type& operation, expression_node_ptr b0)
         {
            expression_node_ptr branch[1] = { b0 };
            return synthesize_expression<unary_node_t,1>(operation,branch);
         }

         inline expression_node_ptr operator()(const details::operator_type& operation, expression_node_ptr b0, expression_node_ptr b1)
         {
            expression_node_ptr branch[2] = { b0, b1 };
            if ((0 == b0) || (0 == b1))
               return error_node();
            else
               return expression_generator<Type>::operator()(operation,branch);
         }

         inline expression_node_ptr conditional(expression_node_ptr condition,
                                                expression_node_ptr consequent,
                                                expression_node_ptr alternative) const
         {
            //Can the condition be immediately evaluated? if so optimize.
            if ((0 == condition) || (0 == consequent) || (0 == alternative))
               return error_node();
            else if (details::is_constant_node(condition))
            {
               // True branch
               if (Type(0) != condition->value())
               {
                  node_allocator_->free(condition);
                  node_allocator_->free(alternative);
                  return consequent;
               }
               // False branch
               else
               {
                  node_allocator_->free(condition);
                  node_allocator_->free(consequent);
                  return alternative;
               }
            }
            else
               return node_allocator_->allocate<conditional_node_t>(condition,consequent,alternative);
         }

         inline expression_node_ptr while_loop(expression_node_ptr condition,
                                               expression_node_ptr branch) const
         {
            return node_allocator_->allocate<while_loop_node_t>(condition,branch);
         }

         inline expression_node_ptr synthesize_uv_expression(const details::operator_type& operation, expression_node_ptr (&branch)[1])
         {
            T& v = dynamic_cast<details::variable_node<T>*>(branch[0])->ref();
            switch (operation)
            {
               #define case_stmt(op0,op1) case op0 : return node_allocator_->allocate<typename details::unary_variable_node<Type,op1<Type> > >(v);
               case_stmt(details::  e_abs,details::  abs_op)
               case_stmt(details:: e_acos,details:: acos_op)
               case_stmt(details:: e_asin,details:: asin_op)
               case_stmt(details:: e_atan,details:: atan_op)
               case_stmt(details:: e_ceil,details:: ceil_op)
               case_stmt(details::  e_cos,details::  cos_op)
               case_stmt(details:: e_cosh,details:: cosh_op)
               case_stmt(details::  e_exp,details::  exp_op)
               case_stmt(details::e_floor,details::floor_op)
               case_stmt(details::  e_log,details::  log_op)
               case_stmt(details::e_log10,details::log10_op)
               case_stmt(details::  e_neg,details::  neg_op)
               case_stmt(details::  e_pos,details::  pos_op)
               case_stmt(details::e_round,details::round_op)
               case_stmt(details::  e_sin,details::  sin_op)
               case_stmt(details:: e_sinh,details:: sinh_op)
               case_stmt(details:: e_sqrt,details:: sqrt_op)
               case_stmt(details::  e_tan,details::  tan_op)
               case_stmt(details:: e_tanh,details:: tanh_op)
               case_stmt(details::  e_cot,details::  cot_op)
               case_stmt(details::  e_sec,details::  sec_op)
               case_stmt(details::  e_csc,details::  csc_op)
               case_stmt(details::  e_r2d,details::  r2d_op)
               case_stmt(details::  e_d2r,details::  d2r_op)
               case_stmt(details::  e_d2g,details::  d2g_op)
               case_stmt(details::  e_g2d,details::  g2d_op)
               case_stmt(details:: e_notl,details:: notl_op)
               case_stmt(details::  e_sgn,details::  sgn_op)
               case_stmt(details::  e_erf,details::  erf_op)
               case_stmt(details:: e_erfc,details:: erfc_op)
               #undef case_stmt
               default : return error_node();
            }
         }

         inline expression_node_ptr synthesize_unary_expression(const details::operator_type& operation, expression_node_ptr (&branch)[1])
         {
            switch (operation)
            {
               #define case_stmt(op0,op1) case op0 : return node_allocator_->allocate<typename details::unary_branch_node<Type,op1<Type> > >(branch[0]);
               case_stmt(details::  e_abs,details::  abs_op)
               case_stmt(details:: e_acos,details:: acos_op)
               case_stmt(details:: e_asin,details:: asin_op)
               case_stmt(details:: e_atan,details:: atan_op)
               case_stmt(details:: e_ceil,details:: ceil_op)
               case_stmt(details::  e_cos,details::  cos_op)
               case_stmt(details:: e_cosh,details:: cosh_op)
               case_stmt(details::  e_exp,details::  exp_op)
               case_stmt(details::e_floor,details::floor_op)
               case_stmt(details::  e_log,details::  log_op)
               case_stmt(details::e_log10,details::log10_op)
               case_stmt(details::  e_neg,details::  neg_op)
               case_stmt(details::  e_pos,details::  pos_op)
               case_stmt(details::e_round,details::round_op)
               case_stmt(details::  e_sin,details::  sin_op)
               case_stmt(details:: e_sinh,details:: sinh_op)
               case_stmt(details:: e_sqrt,details:: sqrt_op)
               case_stmt(details::  e_tan,details::  tan_op)
               case_stmt(details:: e_tanh,details:: tanh_op)
               case_stmt(details::  e_cot,details::  cot_op)
               case_stmt(details::  e_sec,details::  sec_op)
               case_stmt(details::  e_csc,details::  csc_op)
               case_stmt(details::  e_r2d,details::  r2d_op)
               case_stmt(details::  e_d2r,details::  d2r_op)
               case_stmt(details::  e_d2g,details::  d2g_op)
               case_stmt(details::  e_g2d,details::  g2d_op)
               case_stmt(details:: e_notl,details:: notl_op)
               case_stmt(details::  e_sgn,details::  sgn_op)
               case_stmt(details::  e_erf,details::  erf_op)
               case_stmt(details:: e_erfc,details:: erfc_op)
               #undef case_stmt
               default : return error_node();
            }
         }

         inline expression_node_ptr const_optimize_sf3(const details::operator_type& operation, expression_node_ptr (&branch)[3])
         {
            expression_node_ptr temp_node = error_node();
            switch (operation)
            {
               #define case_stmt(op0,op1) case op0 : temp_node = node_allocator_->allocate<details::sf3_node<Type,op1<Type> > >(operation,branch); break;
               case_stmt(details::e_sf00,details::sf00_op)
               case_stmt(details::e_sf01,details::sf01_op)
               case_stmt(details::e_sf02,details::sf02_op)
               case_stmt(details::e_sf03,details::sf03_op)
               case_stmt(details::e_sf04,details::sf04_op)
               case_stmt(details::e_sf05,details::sf05_op)
               case_stmt(details::e_sf06,details::sf06_op)
               case_stmt(details::e_sf07,details::sf07_op)
               case_stmt(details::e_sf08,details::sf08_op)
               case_stmt(details::e_sf09,details::sf09_op)
               case_stmt(details::e_sf10,details::sf10_op)
               case_stmt(details::e_sf11,details::sf11_op)
               case_stmt(details::e_sf12,details::sf12_op)
               case_stmt(details::e_sf13,details::sf13_op)
               case_stmt(details::e_sf14,details::sf14_op)
               case_stmt(details::e_sf15,details::sf15_op)
               case_stmt(details::e_sf16,details::sf16_op)
               case_stmt(details::e_sf17,details::sf17_op)
               case_stmt(details::e_sf18,details::sf18_op)
               case_stmt(details::e_sf19,details::sf19_op)
               case_stmt(details::e_sf20,details::sf20_op)
               case_stmt(details::e_sf21,details::sf21_op)
               case_stmt(details::e_sf22,details::sf22_op)
               case_stmt(details::e_sf23,details::sf23_op)
               case_stmt(details::e_sf24,details::sf24_op)
               case_stmt(details::e_sf25,details::sf25_op)
               case_stmt(details::e_sf26,details::sf26_op)
               case_stmt(details::e_sf27,details::sf27_op)
               case_stmt(details::e_sf28,details::sf28_op)
               case_stmt(details::e_sf29,details::sf29_op)
               case_stmt(details::e_sf30,details::sf30_op)
               case_stmt(details::e_sf31,details::sf31_op)
               case_stmt(details::e_sf32,details::sf32_op)
               case_stmt(details::e_sf33,details::sf33_op)
               case_stmt(details::e_sf34,details::sf34_op)
               #undef case_stmt
               default : return error_node();
            }
            T v = temp_node->value();
            node_allocator_->free(temp_node);
            return node_allocator_->allocate<literal_node_t>(v);
         }

         inline expression_node_ptr special_function(const details::operator_type& operation, expression_node_ptr (&branch)[3])
         {
            if (!all_nodes_valid(branch))
               return error_node();
            else if (is_constant_foldable(branch))
               return const_optimize_sf3(operation,branch);
            switch (operation)
            {
               #define case_stmt(op0,op1) case op0 : return node_allocator_->allocate<details::sf3_node<Type,op1<Type> > >(operation,branch);
               case_stmt(details::e_sf00,details::sf00_op)
               case_stmt(details::e_sf01,details::sf01_op)
               case_stmt(details::e_sf02,details::sf02_op)
               case_stmt(details::e_sf03,details::sf03_op)
               case_stmt(details::e_sf04,details::sf04_op)
               case_stmt(details::e_sf05,details::sf05_op)
               case_stmt(details::e_sf06,details::sf06_op)
               case_stmt(details::e_sf07,details::sf07_op)
               case_stmt(details::e_sf08,details::sf08_op)
               case_stmt(details::e_sf09,details::sf09_op)
               case_stmt(details::e_sf10,details::sf10_op)
               case_stmt(details::e_sf11,details::sf11_op)
               case_stmt(details::e_sf12,details::sf12_op)
               case_stmt(details::e_sf13,details::sf13_op)
               case_stmt(details::e_sf14,details::sf14_op)
               case_stmt(details::e_sf15,details::sf15_op)
               case_stmt(details::e_sf16,details::sf16_op)
               case_stmt(details::e_sf17,details::sf17_op)
               case_stmt(details::e_sf18,details::sf18_op)
               case_stmt(details::e_sf19,details::sf19_op)
               case_stmt(details::e_sf20,details::sf20_op)
               case_stmt(details::e_sf21,details::sf21_op)
               case_stmt(details::e_sf22,details::sf22_op)
               case_stmt(details::e_sf23,details::sf23_op)
               case_stmt(details::e_sf24,details::sf24_op)
               case_stmt(details::e_sf25,details::sf25_op)
               case_stmt(details::e_sf26,details::sf26_op)
               case_stmt(details::e_sf27,details::sf27_op)
               case_stmt(details::e_sf28,details::sf28_op)
               case_stmt(details::e_sf29,details::sf29_op)
               case_stmt(details::e_sf30,details::sf30_op)
               case_stmt(details::e_sf31,details::sf31_op)
               case_stmt(details::e_sf32,details::sf32_op)
               case_stmt(details::e_sf33,details::sf33_op)
               case_stmt(details::e_sf34,details::sf34_op)
               #undef case_stmt
               default : return error_node();
            }
         }

         inline expression_node_ptr const_optimize_sf4(const details::operator_type& operation, expression_node_ptr (&branch)[4])
         {
            expression_node_ptr temp_node = error_node();
            switch (operation)
            {
               #define case_stmt(op0,op1) case op0 : temp_node = node_allocator_->allocate<details::sf4_node<Type,op1<Type> > >(operation,branch); break;
               case_stmt(details::e_sf35,details::sf35_op)
               case_stmt(details::e_sf36,details::sf36_op)
               case_stmt(details::e_sf37,details::sf37_op)
               case_stmt(details::e_sf38,details::sf38_op)
               case_stmt(details::e_sf39,details::sf39_op)
               case_stmt(details::e_sf40,details::sf40_op)
               case_stmt(details::e_sf41,details::sf41_op)
               case_stmt(details::e_sf42,details::sf42_op)
               case_stmt(details::e_sf43,details::sf43_op)
               case_stmt(details::e_sf44,details::sf44_op)
               case_stmt(details::e_sf45,details::sf45_op)
               case_stmt(details::e_sf46,details::sf46_op)
               case_stmt(details::e_sf47,details::sf47_op)
               case_stmt(details::e_sf48,details::sf48_op)
               case_stmt(details::e_sf49,details::sf49_op)
               case_stmt(details::e_sf50,details::sf50_op)
               case_stmt(details::e_sf51,details::sf51_op)
               case_stmt(details::e_sf52,details::sf52_op)
               case_stmt(details::e_sf53,details::sf53_op)
               case_stmt(details::e_sf54,details::sf54_op)
               case_stmt(details::e_sf55,details::sf55_op)
               case_stmt(details::e_sf56,details::sf56_op)
               case_stmt(details::e_sf57,details::sf57_op)
               case_stmt(details::e_sf58,details::sf58_op)
               case_stmt(details::e_sf59,details::sf59_op)
               case_stmt(details::e_sf60,details::sf60_op)
               case_stmt(details::e_sf61,details::sf61_op)
               case_stmt(details::e_sf62,details::sf62_op)
               case_stmt(details::e_sf63,details::sf63_op)
               case_stmt(details::e_sf64,details::sf64_op)
               case_stmt(details::e_sf65,details::sf65_op)
               case_stmt(details::e_sf66,details::sf66_op)
               case_stmt(details::e_sf67,details::sf67_op)
               case_stmt(details::e_sf68,details::sf68_op)
               case_stmt(details::e_sf69,details::sf69_op)
               case_stmt(details::e_sf70,details::sf70_op)
               case_stmt(details::e_sf71,details::sf71_op)
               case_stmt(details::e_sf72,details::sf72_op)
               case_stmt(details::e_sf73,details::sf73_op)
               case_stmt(details::e_sf74,details::sf74_op)
               case_stmt(details::e_sf75,details::sf75_op)
               case_stmt(details::e_sf76,details::sf76_op)
               case_stmt(details::e_sf77,details::sf77_op)
               case_stmt(details::e_sf78,details::sf78_op)
               case_stmt(details::e_sf79,details::sf79_op)
               case_stmt(details::e_sf80,details::sf80_op)
               case_stmt(details::e_sf81,details::sf81_op)
               case_stmt(details::e_sf82,details::sf82_op)
               case_stmt(details::e_sf83,details::sf83_op)
               #undef case_stmt
               default : return error_node();
            }
            T v = temp_node->value();
            node_allocator_->free(temp_node);
            return node_allocator_->allocate<literal_node_t>(v);
         }

         inline expression_node_ptr special_function(const details::operator_type& operation, expression_node_ptr (&branch)[4])
         {
            if (!all_nodes_valid(branch))
               return error_node();
            else if (is_constant_foldable(branch))
               return const_optimize_sf4(operation,branch);
            switch (operation)
            {
               #define case_stmt(op0,op1) case op0 : return node_allocator_->allocate<details::sf4_node<Type,op1<Type> > >(operation,branch);
               case_stmt(details::e_sf35,details::sf35_op)
               case_stmt(details::e_sf36,details::sf36_op)
               case_stmt(details::e_sf37,details::sf37_op)
               case_stmt(details::e_sf38,details::sf38_op)
               case_stmt(details::e_sf39,details::sf39_op)
               case_stmt(details::e_sf40,details::sf40_op)
               case_stmt(details::e_sf41,details::sf41_op)
               case_stmt(details::e_sf42,details::sf42_op)
               case_stmt(details::e_sf43,details::sf43_op)
               case_stmt(details::e_sf44,details::sf44_op)
               case_stmt(details::e_sf45,details::sf45_op)
               case_stmt(details::e_sf46,details::sf46_op)
               case_stmt(details::e_sf47,details::sf47_op)
               case_stmt(details::e_sf48,details::sf48_op)
               case_stmt(details::e_sf49,details::sf49_op)
               case_stmt(details::e_sf50,details::sf50_op)
               case_stmt(details::e_sf51,details::sf51_op)
               case_stmt(details::e_sf52,details::sf52_op)
               case_stmt(details::e_sf53,details::sf53_op)
               case_stmt(details::e_sf54,details::sf54_op)
               case_stmt(details::e_sf55,details::sf55_op)
               case_stmt(details::e_sf56,details::sf56_op)
               case_stmt(details::e_sf57,details::sf57_op)
               case_stmt(details::e_sf58,details::sf58_op)
               case_stmt(details::e_sf59,details::sf59_op)
               case_stmt(details::e_sf60,details::sf60_op)
               case_stmt(details::e_sf61,details::sf61_op)
               case_stmt(details::e_sf62,details::sf62_op)
               case_stmt(details::e_sf63,details::sf63_op)
               case_stmt(details::e_sf64,details::sf64_op)
               case_stmt(details::e_sf65,details::sf65_op)
               case_stmt(details::e_sf66,details::sf66_op)
               case_stmt(details::e_sf67,details::sf67_op)
               case_stmt(details::e_sf68,details::sf68_op)
               case_stmt(details::e_sf69,details::sf69_op)
               case_stmt(details::e_sf70,details::sf70_op)
               case_stmt(details::e_sf71,details::sf71_op)
               case_stmt(details::e_sf72,details::sf72_op)
               case_stmt(details::e_sf73,details::sf73_op)
               case_stmt(details::e_sf74,details::sf74_op)
               case_stmt(details::e_sf75,details::sf75_op)
               case_stmt(details::e_sf76,details::sf76_op)
               case_stmt(details::e_sf77,details::sf77_op)
               case_stmt(details::e_sf78,details::sf78_op)
               case_stmt(details::e_sf79,details::sf79_op)
               case_stmt(details::e_sf80,details::sf80_op)
               case_stmt(details::e_sf81,details::sf81_op)
               case_stmt(details::e_sf82,details::sf82_op)
               case_stmt(details::e_sf83,details::sf83_op)
               #undef case_stmt
               default : return error_node();
            }
         }

         template <std::size_t N>
         inline expression_node_ptr function(ifunction_t* f, expression_node_ptr (&b)[N])
         {
            typedef typename details::function_N_node<T,ifunction_t,N> function_N_node_t;

            expression_node_ptr result = synthesize_expression<function_N_node_t,N>(f,b);
            if (0 == result)
               return error_node();
            else
            {
               //has the function call been completely optimized?
               if (details::is_constant_node(result))
                  return result;
               else if (!all_nodes_valid(b))
                  return error_node();
               else if (N != f->param_count)
                  return error_node();
               function_N_node_t* func_node_ptr = dynamic_cast<function_N_node_t*>(result);
               if (func_node_ptr)
               {
                  if (func_node_ptr->init_branches(b))
                     return result;
                  else
                     return error_node();
               }
               else
                  return error_node();
            }
         }

         inline expression_node_ptr function(ifunction_t* f)
         {
            typedef typename details::function_N_node<T,ifunction_t,0> function_N_node_t;
            return node_allocator_->allocate<function_N_node_t>(f);
         }

      private:

         template <std::size_t N, typename NodePtr>
         inline bool is_constant_foldable(NodePtr (&b)[N]) const
         {
            for (std::size_t i = 0; i < N; ++i)
            {
               if (0 == b[i])
                  return false;
               else if (!details::is_constant_node(b[i]))
                  return false;
            }
            return true;
         }

         template <std::size_t N>
         inline bool all_nodes_valid(expression_node_ptr (&b)[N]) const
         {
            for (std::size_t i = 0; i < N; ++i)
            {
               if (0 == b[i]) return false;
            }
            return true;
         }

         inline expression_node_ptr synthesize_assignment_expression(const details::operator_type& operation, expression_node_ptr (&branch)[2])
         {
            if (details::is_variable_node(branch[0]))
               return synthesize_expression<assignment_node_t,2>(operation,branch);
            else
               return error_node();
         }

         inline expression_node_ptr synthesize_cov_expression(const details::operator_type& operation, expression_node_ptr (&branch)[2])
         {
            T  c = dynamic_cast<details::literal_node<T>* >(branch[0])->value();
            T& v = dynamic_cast<details::variable_node<T>*>(branch[1])->ref();
            node_allocator_->free(branch[0]);
            switch (operation)
            {
               #define case_stmt(op0,op1) case op0 : return node_allocator_->allocate_cr<typename details::cov_node<Type,op1<Type> > >(c,v);
               case_stmt(details:: e_add,details:: add_op)
               case_stmt(details:: e_sub,details:: sub_op)
               case_stmt(details:: e_mul,details:: mul_op)
               case_stmt(details:: e_div,details:: div_op)
               case_stmt(details:: e_mod,details:: mod_op)
               case_stmt(details:: e_pow,details:: pow_op)
               #ifndef exprtk_disable_extended_operator_optimizations
               case_stmt(details::  e_lt,details::  lt_op)
               case_stmt(details:: e_lte,details:: lte_op)
               case_stmt(details::  e_gt,details::  gt_op)
               case_stmt(details:: e_gte,details:: gte_op)
               case_stmt(details::  e_eq,details::  eq_op)
               case_stmt(details::  e_ne,details::  ne_op)
               case_stmt(details:: e_and,details:: and_op)
               case_stmt(details::e_nand,details::nand_op)
               case_stmt(details::  e_or,details::  or_op)
               case_stmt(details:: e_nor,details:: nor_op)
               case_stmt(details:: e_xor,details:: xor_op)
               #endif
               #undef case_stmt
               default : return error_node();
            }
         }

         #ifndef exprtk_disable_cardinal_pow_optimisation
         inline expression_node_ptr cardinal_pow_optimization(T& v, const T& c)
         {
            const bool not_recipricol = (c >= T(0.0));
            const unsigned int p = static_cast<unsigned int>(std::abs(c));
            if (0 == p)
               return node_allocator_->allocate_c<literal_node_t>(T(1.0));
            else
            {
               switch(p)
               {
                  #define case_stmt(cp) case cp : return node_allocator_->allocate_rc<typename details::ipow_node<T,details::numeric::fast_exp<T,cp> > >(v,not_recipricol);
                  case_stmt( 1) case_stmt( 2) case_stmt( 3) case_stmt( 4)
                  case_stmt( 5) case_stmt( 6) case_stmt( 7) case_stmt( 8)
                  case_stmt( 9) case_stmt(10) case_stmt(11) case_stmt(12)
                  case_stmt(13) case_stmt(14) case_stmt(15) case_stmt(16)
                  case_stmt(17) case_stmt(18) case_stmt(19) case_stmt(20)
                  case_stmt(21) case_stmt(22) case_stmt(23) case_stmt(24)
                  case_stmt(25) case_stmt(26) case_stmt(27) case_stmt(28)
                  case_stmt(29) case_stmt(30) case_stmt(31) case_stmt(32)
                  case_stmt(33) case_stmt(34) case_stmt(35) case_stmt(36)
                  case_stmt(37) case_stmt(38) case_stmt(39) case_stmt(40)
                  case_stmt(41) case_stmt(42) case_stmt(43) case_stmt(44)
                  case_stmt(45) case_stmt(46) case_stmt(47) case_stmt(48)
                  case_stmt(49) case_stmt(50) case_stmt(51) case_stmt(52)
                  case_stmt(53) case_stmt(54) case_stmt(55) case_stmt(56)
                  case_stmt(57) case_stmt(58) case_stmt(59) case_stmt(60)
                  #undef case_stmt
                  default : return error_node();
               }
            }
         }

         inline bool cardinal_pow_optimizable(const details::operator_type& operation, const T& c)
         {
            return (details::e_pow == operation) && (std::abs(c) <= T(60.0)) && details::numeric::is_integer(c);
         }
         #else
         inline expression_node_ptr cardinal_pow_optimization(T&, const T&)
         {
            return error_node();
         }

         inline bool cardinal_pow_optimizable(const details::operator_type&, const T&)
         {
            return false;
         }
         #endif

         inline expression_node_ptr synthesize_voc_expression(const details::operator_type& operation, expression_node_ptr (&branch)[2])
         {
            T& v = dynamic_cast<details::variable_node<T>*>(branch[0])->ref();
            T  c = dynamic_cast<details::literal_node<T>* >(branch[1])->value();
            node_allocator_->free(branch[1]);
            if (cardinal_pow_optimizable(operation,c))
            {
               return cardinal_pow_optimization(v,c);
            }

            switch (operation)
            {
               #define case_stmt(op0,op1) case op0 : return node_allocator_->allocate_rc<typename details::voc_node<Type,op1<Type> > >(v,c);
               case_stmt(details:: e_add,details:: add_op)
               case_stmt(details:: e_sub,details:: sub_op)
               case_stmt(details:: e_mul,details:: mul_op)
               case_stmt(details:: e_div,details:: div_op)
               case_stmt(details:: e_mod,details:: mod_op)
               case_stmt(details:: e_pow,details:: pow_op)
               #ifndef exprtk_disable_extended_operator_optimizations
               case_stmt(details::  e_lt,details::  lt_op)
               case_stmt(details:: e_lte,details:: lte_op)
               case_stmt(details::  e_gt,details::  gt_op)
               case_stmt(details:: e_gte,details:: gte_op)
               case_stmt(details::  e_eq,details::  eq_op)
               case_stmt(details::  e_ne,details::  ne_op)
               case_stmt(details:: e_and,details:: and_op)
               case_stmt(details::e_nand,details::nand_op)
               case_stmt(details::  e_or,details::  or_op)
               case_stmt(details:: e_nor,details:: nor_op)
               case_stmt(details:: e_xor,details:: xor_op)
               #endif
               #undef case_stmt
               default : return error_node();
            }
         }

         inline expression_node_ptr synthesize_vov_expression(const details::operator_type& operation, expression_node_ptr (&branch)[2])
         {
            Type& v1 = dynamic_cast<details::variable_node<Type>*>(branch[0])->ref();
            Type& v2 = dynamic_cast<details::variable_node<Type>*>(branch[1])->ref();
            switch (operation)
            {
               #define case_stmt(op0,op1) case op0 : return node_allocator_->allocate_rr<typename details::vov_node<Type,op1<Type> > >(v1,v2);
               case_stmt(details:: e_add,details:: add_op)
               case_stmt(details:: e_sub,details:: sub_op)
               case_stmt(details:: e_mul,details:: mul_op)
               case_stmt(details:: e_div,details:: div_op)
               case_stmt(details:: e_mod,details:: mod_op)
               case_stmt(details:: e_pow,details:: pow_op)
               #ifndef exprtk_disable_extended_operator_optimizations
               case_stmt(details::  e_lt,details::  lt_op)
               case_stmt(details:: e_lte,details:: lte_op)
               case_stmt(details::  e_gt,details::  gt_op)
               case_stmt(details:: e_gte,details:: gte_op)
               case_stmt(details::  e_eq,details::  eq_op)
               case_stmt(details::  e_ne,details::  ne_op)
               case_stmt(details:: e_and,details:: and_op)
               case_stmt(details::e_nand,details::nand_op)
               case_stmt(details::  e_or,details::  or_op)
               case_stmt(details:: e_nor,details:: nor_op)
               case_stmt(details:: e_xor,details:: xor_op)
               #endif
               #undef case_stmt
               default : return error_node();
            }
         }

         template <typename Operation1>
         inline expression_node_ptr synthesize_vovov1_expression_impl(Type& v0, expression_node_ptr node)
         {
            details::operator_type op = dynamic_cast<details::vov_base_node<Type>*>(node)->operation();
            switch (op)
            {
               #define case_stmt(op0,op1) case op0 : return node_allocator_->allocate_rr<typename details::vovov1_node<Type,Operation1,op1<Type> > >(v0,(*dynamic_cast<details::vov_node<T,op1<Type> >*>(node)));
               case_stmt(details:: e_add,details:: add_op)
               case_stmt(details:: e_sub,details:: sub_op)
               case_stmt(details:: e_mul,details:: mul_op)
               case_stmt(details:: e_div,details:: div_op)
               case_stmt(details:: e_mod,details:: mod_op)
               case_stmt(details:: e_pow,details:: pow_op)
               #ifndef exprtk_disable_extended_operator_optimizations
               case_stmt(details::  e_lt,details::  lt_op)
               case_stmt(details:: e_lte,details:: lte_op)
               case_stmt(details::  e_gt,details::  gt_op)
               case_stmt(details:: e_gte,details:: gte_op)
               case_stmt(details::  e_eq,details::  eq_op)
               case_stmt(details::  e_ne,details::  ne_op)
               case_stmt(details:: e_and,details:: and_op)
               case_stmt(details::e_nand,details::nand_op)
               case_stmt(details::  e_or,details::  or_op)
               case_stmt(details:: e_nor,details:: nor_op)
               case_stmt(details:: e_xor,details:: xor_op)
               #endif
               #undef case_stmt
               default : return error_node();
            }
         }

         inline expression_node_ptr synthesize_vovov1_expression(const details::operator_type& operation, expression_node_ptr (&branch)[2])
         {
            T& v0 = dynamic_cast<details::variable_node<T>*>(branch[0])->ref();
            expression_node_ptr result = error_node();
            switch (operation)
            {
               #define case_stmt(op0,op1) case op0 : result = synthesize_vovov1_expression_impl<op1<Type> >(v0,branch[1]); break;
               case_stmt(details:: e_add,details:: add_op)
               case_stmt(details:: e_sub,details:: sub_op)
               case_stmt(details:: e_mul,details:: mul_op)
               case_stmt(details:: e_div,details:: div_op)
               case_stmt(details:: e_mod,details:: mod_op)
               case_stmt(details:: e_pow,details:: pow_op)
               #ifndef exprtk_disable_extended_operator_optimizations
               case_stmt(details::  e_lt,details::  lt_op)
               case_stmt(details:: e_lte,details:: lte_op)
               case_stmt(details::  e_gt,details::  gt_op)
               case_stmt(details:: e_gte,details:: gte_op)
               case_stmt(details::  e_eq,details::  eq_op)
               case_stmt(details::  e_ne,details::  ne_op)
               case_stmt(details:: e_and,details:: and_op)
               case_stmt(details::e_nand,details::nand_op)
               case_stmt(details::  e_or,details::  or_op)
               case_stmt(details:: e_nor,details:: nor_op)
               case_stmt(details:: e_xor,details:: xor_op)
               #endif
               #undef case_stmt
               default : return error_node();
            }
            node_allocator_->free(branch[1]);
            return result;
         }

         template <typename Operation1>
         inline expression_node_ptr synthesize_vovov2_expression_impl(T& v0, expression_node_ptr node)
         {
            details::operator_type op = dynamic_cast<details::vov_base_node<T>*>(node)->operation();
            switch (op)
            {
               #define case_stmt(op0,op1) case op0 : return node_allocator_->allocate_rr<typename details::vovov2_node<T,op1<T>,Operation1> >((*dynamic_cast<details::vov_node<T,op1<T> >*>(node)),v0);
               case_stmt(details:: e_add,details:: add_op)
               case_stmt(details:: e_sub,details:: sub_op)
               case_stmt(details:: e_mul,details:: mul_op)
               case_stmt(details:: e_div,details:: div_op)
               case_stmt(details:: e_mod,details:: mod_op)
               case_stmt(details:: e_pow,details:: pow_op)
               #ifndef exprtk_disable_extended_operator_optimizations
               case_stmt(details::  e_lt,details::  lt_op)
               case_stmt(details:: e_lte,details:: lte_op)
               case_stmt(details::  e_gt,details::  gt_op)
               case_stmt(details:: e_gte,details:: gte_op)
               case_stmt(details::  e_eq,details::  eq_op)
               case_stmt(details::  e_ne,details::  ne_op)
               case_stmt(details:: e_and,details:: and_op)
               case_stmt(details::e_nand,details::nand_op)
               case_stmt(details::  e_or,details::  or_op)
               case_stmt(details:: e_nor,details:: nor_op)
               case_stmt(details:: e_xor,details:: xor_op)
               #endif
               #undef case_stmt
               default : return error_node();
            }
         }

         inline expression_node_ptr synthesize_vovov2_expression(const details::operator_type& operation, expression_node_ptr (&branch)[2])
         {
            T& v0 = dynamic_cast<details::variable_node<T>*>(branch[1])->ref();
            expression_node_ptr result = error_node();
            switch (operation)
            {
               #define case_stmt(op0,op1) case op0 : result = synthesize_vovov2_expression_impl<op1<Type> >(v0,branch[0]); break;
               case_stmt(details:: e_add,details:: add_op)
               case_stmt(details:: e_sub,details:: sub_op)
               case_stmt(details:: e_mul,details:: mul_op)
               case_stmt(details:: e_div,details:: div_op)
               case_stmt(details:: e_mod,details:: mod_op)
               case_stmt(details:: e_pow,details:: pow_op)
               #ifndef exprtk_disable_extended_operator_optimizations
               case_stmt(details::  e_lt,details::  lt_op)
               case_stmt(details:: e_lte,details:: lte_op)
               case_stmt(details::  e_gt,details::  gt_op)
               case_stmt(details:: e_gte,details:: gte_op)
               case_stmt(details::  e_eq,details::  eq_op)
               case_stmt(details::  e_ne,details::  ne_op)
               case_stmt(details:: e_and,details:: and_op)
               case_stmt(details::e_nand,details::nand_op)
               case_stmt(details::  e_or,details::  or_op)
               case_stmt(details:: e_nor,details:: nor_op)
               case_stmt(details:: e_xor,details:: xor_op)
               #endif
               #undef case_stmt
               default : return error_node();
            }
            node_allocator_->free(branch[0]);
            return result;
         }

         template <typename Operation1>
         inline expression_node_ptr synthesize_covov1_expression_impl(const T& c, expression_node_ptr node)
         {
            details::operator_type op = dynamic_cast<details::vov_base_node<T>*>(node)->operation();
            switch (op)
            {
               #define case_stmt(op0,op1) case op0 : return node_allocator_->allocate_rr<typename details::covov1_node<Type,Operation1,op1<Type> > >(c,(*dynamic_cast<details::vov_node<T,op1<T> >*>(node)));
               case_stmt(details:: e_add,details:: add_op)
               case_stmt(details:: e_sub,details:: sub_op)
               case_stmt(details:: e_mul,details:: mul_op)
               case_stmt(details:: e_div,details:: div_op)
               case_stmt(details:: e_mod,details:: mod_op)
               case_stmt(details:: e_pow,details:: pow_op)
               #ifndef exprtk_disable_extended_operator_optimizations
               case_stmt(details::  e_lt,details::  lt_op)
               case_stmt(details:: e_lte,details:: lte_op)
               case_stmt(details::  e_gt,details::  gt_op)
               case_stmt(details:: e_gte,details:: gte_op)
               case_stmt(details::  e_eq,details::  eq_op)
               case_stmt(details::  e_ne,details::  ne_op)
               case_stmt(details:: e_and,details:: and_op)
               case_stmt(details::e_nand,details::nand_op)
               case_stmt(details::  e_or,details::  or_op)
               case_stmt(details:: e_nor,details:: nor_op)
               case_stmt(details:: e_xor,details:: xor_op)
               #endif
               #undef case_stmt
               default : return error_node();
            }
         }

         inline expression_node_ptr synthesize_covov1_expression(const details::operator_type& operation, expression_node_ptr (&branch)[2])
         {
            T c = dynamic_cast<details::literal_node<Type>*>(branch[0])->value();
            expression_node_ptr result = error_node();
            switch (operation)
            {
               #define case_stmt(op0,op1) case op0 : result = synthesize_covov1_expression_impl<op1<Type> >(c,branch[1]); break;
               case_stmt(details:: e_add,details:: add_op)
               case_stmt(details:: e_sub,details:: sub_op)
               case_stmt(details:: e_mul,details:: mul_op)
               case_stmt(details:: e_div,details:: div_op)
               case_stmt(details:: e_mod,details:: mod_op)
               case_stmt(details:: e_pow,details:: pow_op)
               #ifndef exprtk_disable_extended_operator_optimizations
               case_stmt(details::  e_lt,details::  lt_op)
               case_stmt(details:: e_lte,details:: lte_op)
               case_stmt(details::  e_gt,details::  gt_op)
               case_stmt(details:: e_gte,details:: gte_op)
               case_stmt(details::  e_eq,details::  eq_op)
               case_stmt(details::  e_ne,details::  ne_op)
               case_stmt(details:: e_and,details:: and_op)
               case_stmt(details::e_nand,details::nand_op)
               case_stmt(details::  e_or,details::  or_op)
               case_stmt(details:: e_nor,details:: nor_op)
               case_stmt(details:: e_xor,details:: xor_op)
               #endif
               #undef case_stmt
               default : return error_node();
            }
            node_allocator_->free(branch[1]);
            return result;
         }

         template <typename Operation2>
         inline expression_node_ptr synthesize_covov2_expression_impl(expression_node_ptr node, T& v)
         {
            details::operator_type op = dynamic_cast<details::cov_base_node<T>*>(node)->operation();
            switch (op)
            {
               #define case_stmt(op0,op1) case op0 : return node_allocator_->allocate_rr<typename details::covov2_node<Type,op1<T>,Operation2> >((*dynamic_cast<details::cov_node<T,op1<T> >*>(node)),v);
               case_stmt(details:: e_add,details:: add_op)
               case_stmt(details:: e_sub,details:: sub_op)
               case_stmt(details:: e_mul,details:: mul_op)
               case_stmt(details:: e_div,details:: div_op)
               case_stmt(details:: e_mod,details:: mod_op)
               case_stmt(details:: e_pow,details:: pow_op)
               #ifndef exprtk_disable_extended_operator_optimizations
               case_stmt(details::  e_lt,details::  lt_op)
               case_stmt(details:: e_lte,details:: lte_op)
               case_stmt(details::  e_gt,details::  gt_op)
               case_stmt(details:: e_gte,details:: gte_op)
               case_stmt(details::  e_eq,details::  eq_op)
               case_stmt(details::  e_ne,details::  ne_op)
               case_stmt(details:: e_and,details:: and_op)
               case_stmt(details::e_nand,details::nand_op)
               case_stmt(details::  e_or,details::  or_op)
               case_stmt(details:: e_nor,details:: nor_op)
               case_stmt(details:: e_xor,details:: xor_op)
               #endif
               #undef case_stmt
               default : return error_node();
            }
         }

         inline expression_node_ptr synthesize_covov2_expression(const details::operator_type& operation, expression_node_ptr (&branch)[2])
         {
            T& v = dynamic_cast<details::variable_node<Type>*>(branch[1])->ref();
            expression_node_ptr result = error_node();
            switch (operation)
            {
               #define case_stmt(op0,op1) case op0 : result = synthesize_covov2_expression_impl<op1<Type> >(branch[0],v); break;
               case_stmt(details:: e_add,details:: add_op)
               case_stmt(details:: e_sub,details:: sub_op)
               case_stmt(details:: e_mul,details:: mul_op)
               case_stmt(details:: e_div,details:: div_op)
               case_stmt(details:: e_mod,details:: mod_op)
               case_stmt(details:: e_pow,details:: pow_op)
               #ifndef exprtk_disable_extended_operator_optimizations
               case_stmt(details::  e_lt,details::  lt_op)
               case_stmt(details:: e_lte,details:: lte_op)
               case_stmt(details::  e_gt,details::  gt_op)
               case_stmt(details:: e_gte,details:: gte_op)
               case_stmt(details::  e_eq,details::  eq_op)
               case_stmt(details::  e_ne,details::  ne_op)
               case_stmt(details:: e_and,details:: and_op)
               case_stmt(details::e_nand,details::nand_op)
               case_stmt(details::  e_or,details::  or_op)
               case_stmt(details:: e_nor,details:: nor_op)
               case_stmt(details:: e_xor,details:: xor_op)
               #endif
               #undef case_stmt
               default : return error_node();
            }
            node_allocator_->free(branch[0]);
            return result;
         }

         #ifndef exprtk_disable_extended_optimisations
         template <typename Op1, typename Op2>
         inline expression_node_ptr synthesize_vovovov_expression_impl2(expression_node_ptr (&node)[2])
         {
            details::operator_type op = dynamic_cast<details::vov_base_node<T>*>(node[1])->operation();
            switch (op)
            {
               #define case_stmt(op0,op1) case op0 : return node_allocator_->allocate_rr<typename details::vovovov_node<Type,Op1,Op2,op1<T> > >((*dynamic_cast<details::vov_node<T,Op1>*>(node[0])),(*dynamic_cast<details::vov_node<T,op1<T> >*>(node[1])));
               case_stmt(details:: e_add,details:: add_op)
               case_stmt(details:: e_sub,details:: sub_op)
               case_stmt(details:: e_mul,details:: mul_op)
               case_stmt(details:: e_div,details:: div_op)
               case_stmt(details:: e_mod,details:: mod_op)
               case_stmt(details:: e_pow,details:: pow_op)
               #ifndef exprtk_disable_extended_operator_optimizations
               case_stmt(details::  e_lt,details::  lt_op)
               case_stmt(details:: e_lte,details:: lte_op)
               case_stmt(details::  e_gt,details::  gt_op)
               case_stmt(details:: e_gte,details:: gte_op)
               case_stmt(details::  e_eq,details::  eq_op)
               case_stmt(details::  e_ne,details::  ne_op)
               case_stmt(details:: e_and,details:: and_op)
               case_stmt(details::e_nand,details::nand_op)
               case_stmt(details::  e_or,details::  or_op)
               case_stmt(details:: e_nor,details:: nor_op)
               case_stmt(details:: e_xor,details:: xor_op)
               #endif
               #undef case_stmt
               default : return error_node();
            }
         #else
         template <typename Op1, typename Op2>
         inline expression_node_ptr synthesize_vovovov_expression_impl2(expression_node_ptr (&)[2])
         {
            return error_node();
         #endif
         }

         #ifndef exprtk_disable_extended_optimisations
         template <typename Operation2>
         inline expression_node_ptr synthesize_vovovov_expression_impl1(expression_node_ptr (&node)[2])
         {
            details::operator_type op = dynamic_cast<details::vov_base_node<T>*>(node[0])->operation();
            switch (op)
            {
               #define case_stmt(op0,op1) case op0 : return synthesize_vovovov_expression_impl2<op1<T>,Operation2>(node); break;
               case_stmt(details:: e_add,details:: add_op)
               case_stmt(details:: e_sub,details:: sub_op)
               case_stmt(details:: e_mul,details:: mul_op)
               case_stmt(details:: e_div,details:: div_op)
               case_stmt(details:: e_mod,details:: mod_op)
               case_stmt(details:: e_pow,details:: pow_op)
               #ifndef exprtk_disable_extended_operator_optimizations
               case_stmt(details::  e_lt,details::  lt_op)
               case_stmt(details:: e_lte,details:: lte_op)
               case_stmt(details::  e_gt,details::  gt_op)
               case_stmt(details:: e_gte,details:: gte_op)
               case_stmt(details::  e_eq,details::  eq_op)
               case_stmt(details::  e_ne,details::  ne_op)
               case_stmt(details:: e_and,details:: and_op)
               case_stmt(details::e_nand,details::nand_op)
               case_stmt(details::  e_or,details::  or_op)
               case_stmt(details:: e_nor,details:: nor_op)
               case_stmt(details:: e_xor,details:: xor_op)
               #endif
               #undef case_stmt
               default : return error_node();
            }
         }
         #else
         template <typename Operation2>
         inline expression_node_ptr synthesize_vovovov_expression_impl1(expression_node_ptr (&)[2])
         {
            return error_node();
         }
         #endif

         #ifndef exprtk_disable_extended_optimisations
         inline expression_node_ptr synthesize_vovovov_expression(const details::operator_type& opr, expression_node_ptr (&branch)[2])
         {
            expression_node_ptr result = error_node();
            switch (opr)
            {
               #define case_stmt(op0,op1) case op0 : result = synthesize_vovovov_expression_impl1<op1<T> >(branch); break;
               case_stmt(details:: e_add,details:: add_op)
               case_stmt(details:: e_sub,details:: sub_op)
               case_stmt(details:: e_mul,details:: mul_op)
               case_stmt(details:: e_div,details:: div_op)
               case_stmt(details:: e_mod,details:: mod_op)
               case_stmt(details:: e_pow,details:: pow_op)
               #ifndef exprtk_disable_extended_operator_optimizations
               case_stmt(details::  e_lt,details::  lt_op)
               case_stmt(details:: e_lte,details:: lte_op)
               case_stmt(details::  e_gt,details::  gt_op)
               case_stmt(details:: e_gte,details:: gte_op)
               case_stmt(details::  e_eq,details::  eq_op)
               case_stmt(details::  e_ne,details::  ne_op)
               case_stmt(details:: e_and,details:: and_op)
               case_stmt(details::e_nand,details::nand_op)
               case_stmt(details::  e_or,details::  or_op)
               case_stmt(details:: e_nor,details:: nor_op)
               case_stmt(details:: e_xor,details:: xor_op)
               #endif
               #undef case_stmt
               default : return error_node();
            }
            node_allocator_->free(branch[0]);
            node_allocator_->free(branch[1]);
            return result;
         }
         #else
         inline expression_node_ptr synthesize_vovovov_expression(const details::operator_type&, expression_node_ptr (&)[2])
         {
            return error_node();
         }
         #endif

         #ifndef exprtk_disable_string_capabilities
         template <typename T0, typename T1>
         inline expression_node_ptr synthesize_sos_expression_impl(const details::operator_type& opr, T0 s0, T1 s1)
         {
            switch (opr)
            {
               #define case_stmt(op0,op1) case op0 : return node_allocator_->allocate_tt<typename details::sos_node<Type,T0,T1,op1<Type> >,T0,T1>(s0,s1);
               case_stmt(details::e_lt   ,details::   lt_op)
               case_stmt(details::e_lte  ,details::  lte_op)
               case_stmt(details::e_gt   ,details::   gt_op)
               case_stmt(details::e_gte  ,details::  gte_op)
               case_stmt(details::e_eq   ,details::   eq_op)
               case_stmt(details::e_ne   ,details::   ne_op)
               case_stmt(details::e_in   ,details::   in_op)
               case_stmt(details::e_like ,details:: like_op)
               case_stmt(details::e_ilike,details::ilike_op)
               #undef case_stmt
               default : return error_node();
            }
         }

         inline expression_node_ptr synthesize_sos_expression(const details::operator_type& opr, expression_node_ptr (&branch)[2])
         {
            std::string& s0 = dynamic_cast<details::stringvar_node<Type>*>(branch[0])->ref();
            std::string& s1 = dynamic_cast<details::stringvar_node<Type>*>(branch[1])->ref();
            return synthesize_sos_expression_impl<std::string&,std::string&>(opr,s0,s1);
         }

         inline expression_node_ptr synthesize_socs_expression(const details::operator_type& opr, expression_node_ptr (&branch)[2])
         {
            std::string& s0 = dynamic_cast<     details::stringvar_node<Type>*>(branch[0])->ref();
            std::string  s1 = dynamic_cast<details::string_literal_node<Type>*>(branch[1])->str();
            node_allocator_->free(branch[1]);
            return synthesize_sos_expression_impl<std::string&,const std::string>(opr,s0,s1);
         }

         inline expression_node_ptr synthesize_csos_expression(const details::operator_type& opr, expression_node_ptr (&branch)[2])
         {
            std::string  s0 = dynamic_cast<details::string_literal_node<Type>*>(branch[0])->str();
            std::string& s1 = dynamic_cast<     details::stringvar_node<Type>*>(branch[1])->ref();
            node_allocator_->free(branch[0]);
            return synthesize_sos_expression_impl<const std::string,std::string&>(opr,s0,s1);
         }

         inline expression_node_ptr synthesize_csocs_expression(const details::operator_type& opr, expression_node_ptr (&branch)[2])
         {
            const std::string s0 = dynamic_cast<details::string_literal_node<Type>*>(branch[0])->str();
            const std::string s1 = dynamic_cast<details::string_literal_node<Type>*>(branch[1])->str();
            expression_node_ptr result = error_node();
            if (details::e_add == opr)
               result = node_allocator_->allocate_c<details::string_literal_node<Type> >(s0 + s1);
            else if (details::e_in == opr)
               result = node_allocator_->allocate_c<details::literal_node<Type> >(details::in_op<Type>::process(s0,s1));
            else if (details::e_like == opr)
               result = node_allocator_->allocate_c<details::literal_node<Type> >(details::like_op<Type>::process(s0,s1));
            else if (details::e_ilike == opr)
               result = node_allocator_->allocate_c<details::literal_node<Type> >(details::ilike_op<Type>::process(s0,s1));
            else
            {
               expression_node_ptr temp = synthesize_sos_expression_impl<const std::string,const std::string>(opr,s0,s1);
               Type v = temp->value();
               node_allocator_->free(temp);
               result = node_allocator_->allocate<literal_node_t>(v);
            }
            node_allocator_->free(branch[0]);
            node_allocator_->free(branch[1]);
            return result;
         }
         #endif

         #ifndef exprtk_disable_string_capabilities
         inline expression_node_ptr synthesize_string_expression(const details::operator_type& opr, expression_node_ptr (&branch)[2])
         {
            if (details::is_string_node(branch[0]))
            {
                    if (details::is_string_node(branch[1]))       return synthesize_sos_expression(opr,branch);
               else if (details::is_const_string_node(branch[1])) return synthesize_socs_expression(opr,branch);
            }
            else if (details::is_const_string_node(branch[0]))
            {
                    if (details::is_string_node(branch[1]))       return synthesize_csos_expression(opr,branch);
               else if (details::is_const_string_node(branch[1])) return synthesize_csocs_expression(opr,branch);
            }
            return error_node();
         }
         #else
         inline expression_node_ptr synthesize_string_expression(const details::operator_type&, expression_node_ptr (&)[2])
         {
            return error_node();
         }
         #endif

         #ifndef exprtk_disable_string_capabilities
         inline expression_node_ptr synthesize_string_expression(const details::operator_type& opr, expression_node_ptr (&branch)[3])
         {
            if (details::e_inrange != opr)
               return error_node();
            else if (
                      details::is_const_string_node(branch[0]) &&
                      details::is_const_string_node(branch[1]) &&
                      details::is_const_string_node(branch[2])
                    )
            {
               const std::string s0 = dynamic_cast<details::string_literal_node<Type>*>(branch[0])->str();
               const std::string s1 = dynamic_cast<details::string_literal_node<Type>*>(branch[1])->str();
               const std::string s2 = dynamic_cast<details::string_literal_node<Type>*>(branch[2])->str();
               Type v = (((s0 <= s1) && (s1 <= s2)) ? Type(1) : Type(0));
               node_allocator_->free(branch[0]);
               node_allocator_->free(branch[1]);
               node_allocator_->free(branch[2]);
               return node_allocator_->allocate_c<details::literal_node<Type> >(v);
            }
            else if (
                     details::is_string_node(branch[0]) &&
                     details::is_string_node(branch[1]) &&
                     details::is_string_node(branch[2])
                    )
            {
               std::string& s0 = dynamic_cast<details::stringvar_node<Type>*>(branch[0])->ref();
               std::string& s1 = dynamic_cast<details::stringvar_node<Type>*>(branch[1])->ref();
               std::string& s2 = dynamic_cast<details::stringvar_node<Type>*>(branch[2])->ref();
               typedef typename details::sosos_node<Type,std::string&,std::string&,std::string&,details::inrange_op<Type> > inrange_t;
               return node_allocator_->allocate_type<inrange_t,std::string&,std::string&,std::string&>(s0,s1,s2);
            }
            else if (
                     details::is_const_string_node(branch[0]) &&
                           details::is_string_node(branch[1]) &&
                     details::is_const_string_node(branch[2])
                    )
            {
               std::string  s0 = dynamic_cast<details::string_literal_node<Type>*>(branch[0])->str();
               std::string& s1 = dynamic_cast<     details::stringvar_node<Type>*>(branch[1])->ref();
               std::string  s2 = dynamic_cast<details::string_literal_node<Type>*>(branch[2])->str();
               typedef typename details::sosos_node<Type,std::string,std::string&,std::string,details::inrange_op<Type> > inrange_t;
               node_allocator_->free(branch[0]);
               node_allocator_->free(branch[2]);
               return node_allocator_->allocate_type<inrange_t,std::string,std::string&,std::string>(s0,s1,s2);
            }
            else if (
                           details::is_string_node(branch[0]) &&
                     details::is_const_string_node(branch[1]) &&
                           details::is_string_node(branch[2])
                    )
            {
               std::string&  s0 = dynamic_cast<     details::stringvar_node<Type>*>(branch[0])->ref();
               std::string   s1 = dynamic_cast<details::string_literal_node<Type>*>(branch[1])->str();
               std::string&  s2 = dynamic_cast<     details::stringvar_node<Type>*>(branch[2])->ref();
               typedef typename details::sosos_node<Type,std::string&,std::string,std::string&,details::inrange_op<Type> > inrange_t;
               node_allocator_->free(branch[1]);
               return node_allocator_->allocate_type<inrange_t,std::string&,std::string,std::string&>(s0,s1,s2);
            }
            else if (
                     details::is_string_node(branch[0]) &&
                     details::is_string_node(branch[1]) &&
                     details::is_const_string_node(branch[2])
                    )
            {
               std::string& s0 = dynamic_cast<     details::stringvar_node<Type>*>(branch[0])->ref();
               std::string& s1 = dynamic_cast<     details::stringvar_node<Type>*>(branch[1])->ref();
               std::string  s2 = dynamic_cast<details::string_literal_node<Type>*>(branch[2])->str();
               typedef typename details::sosos_node<Type,std::string&,std::string&,std::string,details::inrange_op<Type> > inrange_t;
               node_allocator_->free(branch[2]);
               return node_allocator_->allocate_type<inrange_t,std::string&,std::string&,std::string>(s0,s1,s2);
            }
            else if (
                     details::is_const_string_node(branch[0]) &&
                     details::      is_string_node(branch[1]) &&
                     details::      is_string_node(branch[2])
                    )
            {
               std::string  s0 = dynamic_cast<details::string_literal_node<Type>*>(branch[0])->str();
               std::string& s1 = dynamic_cast<     details::stringvar_node<Type>*>(branch[1])->ref();
               std::string& s2 = dynamic_cast<     details::stringvar_node<Type>*>(branch[2])->ref();
               typedef typename details::sosos_node<Type,std::string,std::string&,std::string&,details::inrange_op<Type> > inrange_t;
               node_allocator_->free(branch[0]);
               return node_allocator_->allocate_type<inrange_t,std::string,std::string&,std::string&>(s0,s1,s2);
            }
            else
               return error_node();
         }
         #else
         inline expression_node_ptr synthesize_string_expression(const details::operator_type&, expression_node_ptr (&)[3])
         {
            return error_node();
         }
         #endif

         template <typename NodeType, std::size_t N>
         inline expression_node_ptr synthesize_expression(const details::operator_type& operation, expression_node_ptr (&branch)[N])
         {
            if ((details::e_in == operation) || (details::e_like == operation) || (details::e_ilike == operation))
               return error_node();
            else if ((details::e_default != operation) && all_nodes_valid<N>(branch))
            {
               //Attempt simple constant folding optimization.
               expression_node_ptr expression_point = node_allocator_->allocate<NodeType>(operation,branch);
               if (is_constant_foldable<N>(branch))
               {
                  Type v = expression_point->value();
                  node_allocator_->free(expression_point);
                  return node_allocator_->allocate<literal_node_t>(v);
               }
               else
                  return expression_point;
            }
            else
               return error_node();
         }

         template <typename NodeType, std::size_t N>
         inline expression_node_ptr synthesize_expression(F* f, expression_node_ptr (&branch)[N])
         {
            if (all_nodes_valid<N>(branch))
            {
               typedef typename details::function_N_node<T,ifunction_t,N> function_N_node_t;
               //Attempt simple constant folding optimization.
               expression_node_ptr expression_point = node_allocator_->allocate<NodeType>(f);
               dynamic_cast<function_N_node_t*>(expression_point)->init_branches(branch);
               if (is_constant_foldable<N>(branch))
               {
                  Type v = expression_point->value();
                  node_allocator_->free(expression_point);
                  return node_allocator_->allocate<literal_node_t>(v);
               }
               else
                  return expression_point;
            }
            else
               return error_node();
         }

         details::node_allocator* node_allocator_;
         optimization_level optimization_level_;
      };

      template <typename Type>
      class expression_optimizer
      {
      public:

         typedef details::expression_node<Type>* expression_node_ptr;

         inline void set_allocator(details::node_allocator& na)
         {
            node_allocator_ = &na;
         }

         inline void process(expression_node_ptr expr)
         {
            std::deque<expression_node_ptr> node_list;
            node_list.push_back(expr);
            expression_node_ptr node = reinterpret_cast<expression_node_ptr>(0);
            while (!node_list.empty())
            {
               node = node_list.front();
               node_list.pop_front();
               if (details::is_constant_node(node) || details::is_variable_node(node))
                  continue;
               else if (details::is_binary_node(node) && bn_type0_optimizable(node))
                  perform_bn_type0_optimization(node);
               else
                  add_sub_branches(node,node_list);
            }
         }

      private:

         template <typename Allocator,
                   template <typename, typename> class Sequence>
         void add_sub_branches(expression_node_ptr node, Sequence<expression_node_ptr,Allocator>& seq)
         {
            if (details::is_unary_node(node))
               seq.push_back(node->branch(0));
            else if (details::is_binary_node(node))
            {
               seq.push_back(node->branch(0));
               seq.push_back(node->branch(1));
            }
         }

         inline bool operation_optimizable(const details::operator_type& operation) const
         {
            return (details::e_add  == operation) || (details::e_sub  == operation) ||
                   (details::e_mul  == operation) || (details::e_div  == operation) ||
                   (details::e_mod  == operation) || (details::e_pow  == operation) ||
                   (details::e_lt   == operation) || (details::e_lte  == operation) ||
                   (details::e_gt   == operation) || (details::e_gte  == operation) ||
                   (details::e_eq   == operation) || (details::e_ne   == operation) ||
                   (details::e_and  == operation) || (details::e_nand == operation) ||
                   (details::e_or   == operation) || (details::e_nor  == operation) ||
                   (details::e_xor  == operation);
         }

         inline bool bn_type0_optimizable(const expression_node_ptr expr) const
         {
            const details::binary_node<Type>* node = dynamic_cast<const details::binary_node<Type>*>(expr);
            if (0 == node)
               return false;
            else if (!operation_optimizable(node->operation()))
               return false;
            expression_node_ptr b0 = node->branch(0);
            expression_node_ptr b1 = node->branch(1);
            if (details::is_variable_node(b0) && (details::is_variable_node(b1) || details::is_constant_node(b1)))
               return true;
            else if (details::is_constant_node(b0) && (details::is_variable_node(b1) || details::is_constant_node(b1)))
               return true;
            else
               return false;
         }

         inline void perform_bn_type0_optimization(const expression_node_ptr)
         {
         }

      private:

         details::node_allocator* node_allocator_;
      };

      inline bool check0(const char c0, const char c1,
                         const char v0, const char v1,
                         const char v2)
      {
         return ((c0 == v0) && ((c1 == v1) || (c1 == v2)));
      }

      inline bool check1(const char c0, const char c1,
                         const char v0, const char v1)
      {
         return ((c0 == v0) && (c1 == v1));
      }

      inline bool validate_expression(const std::string& expression_string)
      {
         if (expression_string.empty())
         {
            set_error("parser::validate_expression() - empty expression");
            return false;
         }

         //Check for certain illegal sequences of characters.
         std::stack<char> bracket_stack;
         bool in_string = false;
         for (std::size_t i = 0; i < (expression_string.size() - 1); ++i)
         {
            char c0 = expression_string[i];
            char c1 = expression_string[i + 1];
            if ('\'' == c0)
            {
               in_string = !in_string;
               continue;
            }
            else if (in_string)
               continue;
            else if (details::is_invalid(c0))
            {
               set_error(std::string("parser::validate_expression() - invalid character: ") + c0);
               return false;
            }
            else if (
                     check0(c0,c1,'*','*','/') || check0(c0,c1,'*','%','^') ||
                     check0(c0,c1,'/','*','/') || check0(c0,c1,'/','%','^') ||
                     check0(c0,c1,'+','*','/') || check0(c0,c1,'+','%','^') ||
                     check0(c0,c1,'-','*','/') || check0(c0,c1,'-','%','^') ||
                     check0(c0,c1,'^','*','/') || check0(c0,c1,'^','^','%') ||
                     check0(c0,c1,'%','*','/') || check0(c0,c1,'%','^','%') ||
                     check0(c0,c1,'.','%','^') || check0(c0,c1,'.','*','/') ||
                     check0(c0,c1,',','%','^') || check0(c0,c1,',','*','/') ||
                     check0(c0,c1,'(','*','/') || check0(c0,c1,'(','%','^') ||
                     check0(c0,c1,'[','*','/') || check0(c0,c1,'[','%','^') ||
                     check0(c0,c1,'{','*','/') || check0(c0,c1,'{','%','^') ||
                     check0(c0,c1,'+',')',']') || check0(c0,c1,'-',')',']') ||
                     check0(c0,c1,'*',')',']') || check0(c0,c1,'/',')',']') ||
                     check0(c0,c1,'^',')',']') || check0(c0,c1,'%',')',']') ||
                     check1(c0,c1,'+','}'    ) || check1(c0,c1,'-','}'    ) ||
                     check1(c0,c1,'*','}'    ) || check1(c0,c1,'/','}'    ) ||
                     check1(c0,c1,'^','}'    ) || check1(c0,c1,'%','}'    ) ||
                     check1(c0,c1,'.','.'    ) || check1(c0,c1,'.','+'    ) ||
                     check1(c0,c1,'.','-'    ) || check1(c0,c1,'.','*'    ) ||
                     check1(c0,c1,'.','/'    ) || check1(c0,c1,',',','    )
                    )
            {
               set_error(std::string("parser::validate_expression() - invalid character combination: ") + expression_string.substr(i,2));
               return false;
            }
            else if (c0 == '(')
               bracket_stack.push(')');
            else if (c0 == '[')
               bracket_stack.push(']');
            else if (c0 == '{')
               bracket_stack.push('}');
            else if (details::is_right_bracket(c0))
            {
               if (bracket_stack.empty())
               {
                  set_error(std::string("parser::validate_expression() - invalid/mismatched bracket(s)[0]: ") + expression_string.substr(0,i));
                  return false;
               }
               else if (c0 != bracket_stack.top())
               {
                  set_error(std::string("parser::validate_expression() - invalid/mismatched bracket(s)[1]: ") + expression_string.substr(0,i));
                  return false;
               }
               else
                  bracket_stack.pop();
            }
         }

         if (!bracket_stack.empty())
         {
            if (1 == bracket_stack.size())
            {
               char c0 = expression_string[expression_string.size() - 1];
               if (details::is_right_bracket(c0))
               {
                  if (c0 == bracket_stack.top())
                     return true;
                  else
                  {
                     set_error(std::string("parser::validate_expression() - invalid/mismatched bracket(s)[2]: ") + expression_string);
                     return false;
                  }
               }
            }
            set_error(std::string("parser::validate_expression() - invalid/mismatched bracket(s)[3]: ") + expression_string);
            return false;
         }
         return true;
      }

      inline void set_error(const std::string& err_str)
      {
         //would it be better if this were a stack?
         if (error_description_.empty())
         {
            error_description_ = err_str;
         }
      }

   private:

      details::lexer<T> lexer_;
      details::token<T> current_token_;
      details::token<T> store_current_token_;
      expression_generator<T> expression_generator_;
      expression_optimizer<T> expression_optimizer_;
      details::node_allocator node_allocator_;
      symbol_table<T> symbol_table_;
      std::string error_description_;
      bool symbol_name_caching_;
      std::deque<std::string> symbol_name_cache_;
   };

   template <typename T>
   inline T integrate(expression<T>& e,
                      T& x,
                      const T& r0, const T& r1,
                      const std::size_t number_of_intervals = 1000000)
   {
      if (r0 > r1) return T(0);
      T h = (r1 - r0) / (T(2.0) * number_of_intervals);
      T total_area = T(0);
      for (std::size_t i = 0; i < number_of_intervals; ++i)
      {
         x = r0 + T(2.0) * i * h;
         T y0 = e.value(); x += h;
         T y1 = e.value(); x += h;
         T y2 = e.value(); x += h;
         total_area += h * (y0 + T(4.0) * y1 + y2) / T(3.0);
      }
      return total_area;
   }

   template <typename T>
   inline T integrate(expression<T>& e,
                      const std::string& variable_name,
                      const T& r0, const T& r1,
                      const std::size_t number_of_intervals = 1000000)
   {
      symbol_table<T>& sym_table = e.get_symbol_table();
      if (!sym_table.valid())
         return std::numeric_limits<T>::quiet_NaN();
      details::variable_node<T>* var = sym_table.get_variable(variable_name);
      if (var)
      {
         T& x = var->ref();
         T  x_original = x;
         T result = integrate(e,x,r0,r1,number_of_intervals);
         x = x_original;
         return result;
      }
      else
         return std::numeric_limits<T>::quiet_NaN();
   }

   template <typename T>
   inline T derivative(expression<T>& e,
                       T& x,
                       const double& h = 0.00001)
   {
      T x_init = x;
      x = x_init + T(2.0) * h;
      T y0 = e.value();
      x = x_init + h;
      T y1 = e.value();
      x = x_init - h;
      T y2 = e.value();
      x = x_init - T(2.0) * h;
      T y3 = e.value();
      x = x_init;
      return (-y0 + T(8.0) * (y1 - y2) + y3) / (T(12.0) * h);
   }

   template <typename T>
   inline T derivative(expression<T>& e,
                       const std::string& variable_name,
                       const double& h = 0.00001)
   {
      symbol_table<T>& sym_table = e.get_symbol_table();
      if (!sym_table.valid())
         return std::numeric_limits<T>::quiet_NaN();
      details::variable_node<T>* var = sym_table.get_variable(variable_name);
      if (var)
      {
         T& x = var->ref();
         T x_original = x;
         T result = derivative(e,x,h);
         x = x_original;
         return result;
      }
      else
         return std::numeric_limits<T>::quiet_NaN();
   }

   /*
      Note: The following 'compute' routines are very simple helpers,
      for quickly setting up the required pieces of code in order to
      evaluate an expression. By virtue of how they the operate there
      will be an overhead with regards to their setup and teardown and
      hence should not be used in time critical sections of code.
      Furthermore they only assume a small sub set of variables - no
      string variables or user defined functions.
   */
   template <typename T>
   inline bool compute(const std::string& expression_string, T& result)
   {
      //No variables
      symbol_table<T> symbol_table;
      symbol_table.add_constants();
      expression<T> expression;
      parser<T> parser;
      if (parser.compile(expression_string,expression))
      {
         result = expression.value();
         return true;
      }
      else
         return false;
   }

   template <typename T>
   inline bool compute(const std::string& expression_string,
                       const T& x,
                       T& result)
   {
      //Only 'x'
      static const std::string x_var("x");
      symbol_table<T> symbol_table;
      symbol_table.add_constants();
      symbol_table.add_variable("x",x);
      expression<T> expression;
      parser<T> parser;
      if (parser.compile(expression_string,expression))
      {
         result = expression.value();
         return true;
      }
      else
         return false;
   }

   template <typename T>
   inline bool compute(const std::string& expression_string,
                       const T&x, const T& y,
                       T& result)
   {
      //Only 'x' and 'y'
      static const std::string x_var("x");
      static const std::string y_var("y");
      symbol_table<T> symbol_table;
      symbol_table.add_constants();
      symbol_table.add_variable("x",x);
      symbol_table.add_variable("y",y);
      expression<T> expression;
      parser<T> parser;
      if (parser.compile(expression_string,expression))
      {
         result = expression.value();
         return true;
      }
      else
         return false;
   }

   template <typename T>
   inline bool compute(const std::string& expression_string,
                       const T& x, const T& y, const T& z,
                       T& result)
   {
      //Only 'x', 'y' or 'z'
      static const std::string x_var("x");
      static const std::string y_var("y");
      static const std::string z_var("z");
      symbol_table<T> symbol_table;
      symbol_table.add_constants();
      symbol_table.add_variable(x_var,x);
      symbol_table.add_variable(y_var,y);
      symbol_table.add_variable(z_var,z);
      expression<T> expression;
      parser<T> parser;
      if (parser.compile(expression_string,expression))
      {
         result = expression.value();
         return true;
      }
      else
         return false;
   }

   template <typename T, std::size_t N>
   class polynomial : public ifunction<T>
   {
   private:

      template <typename Type, std::size_t NumberOfCoefficients>
      struct poly_impl { };

      template <typename Type>
      struct poly_impl <Type,10>
      {
         static inline T evaluate(const Type x,
                                  const Type c10, const Type c9, const Type c8, const Type c7, const Type c6,
                                  const Type c5,  const Type c4, const Type c3, const Type c2, const Type c1,
                                  const Type c0)
         {
            //p(x) = c_10x^10 + c_9x^9 + c_8x^8 + c_7x^7 + c_6x^6 + c_5x^5 + c_4x^4 + c_3x^3 + c_2x^2 + c_1x^1 + c_0
            return ((((((((((c10 * x + c9) * x + c8) * x + c7) * x + c6) * x + c5) * x + c4) * x + c3) * x + c2) * x + c1) * x + c0);
         }
      };

      template <typename Type>
      struct poly_impl <Type,9>
      {
         static inline T evaluate(const Type x,
                                  const Type c9, const Type c8, const Type c7, const Type c6, const Type c5,
                                  const Type c4, const Type c3, const Type c2, const Type c1, const Type c0)
         {
            //p(x) = c_9x^9 + c_8x^8 + c_7x^7 + c_6x^6 + c_5x^5 + c_4x^4 + c_3x^3 + c_2x^2 + c_1x^1 + c_0
            return (((((((((c9 * x + c8) * x + c7) * x + c6) * x + c5) * x + c4) * x + c3) * x + c2) * x + c1) * x + c0);
         }
      };

      template <typename Type>
      struct poly_impl <Type,8>
      {
         static inline T evaluate(const Type x,
                                  const Type c8, const Type c7, const Type c6, const Type c5, const Type c4,
                                  const Type c3, const Type c2, const Type c1, const Type c0)
         {
            //p(x) = c_8x^8 + c_7x^7 + c_6x^6 + c_5x^5 + c_4x^4 + c_3x^3 + c_2x^2 + c_1x^1 + c_0
            return ((((((((c8 * x + c7) * x + c6) * x + c5) * x + c4) * x + c3) * x + c2) * x + c1) * x + c0);
         }
      };

      template <typename Type>
      struct poly_impl <Type,7>
      {
         static inline T evaluate(const Type x,
                                  const Type c7, const Type c6, const Type c5, const Type c4, const Type c3,
                                  const Type c2, const Type c1, const Type c0)
         {
            //p(x) = c_7x^7 + c_6x^6 + c_5x^5 + c_4x^4 + c_3x^3 + c_2x^2 + c_1x^1 + c_0
            return (((((((c7 * x + c6) * x + c5) * x + c4) * x + c3) * x + c2) * x + c1) * x + c0);
         }
      };

      template <typename Type>
      struct poly_impl <Type,6>
      {
         static inline T evaluate(const Type x,
                                  const Type c6, const Type c5, const Type c4, const Type c3, const Type c2,
                                  const Type c1, const Type c0)
         {
            //p(x) = c_6x^6 + c_5x^5 + c_4x^4 + c_3x^3 + c_2x^2 + c_1x^1 + c_0
            return ((((((c6 * x + c5) * x + c4) * x + c3) * x + c2) * x + c1) * x + c0);
         }
      };

      template <typename Type>
      struct poly_impl <Type,5>
      {
         static inline T evaluate(const Type x,
                                  const Type c5, const Type c4, const Type c3, const Type c2,
                                  const Type c1, const Type c0)
         {
            //p(x) = c_5x^5 + c_4x^4 + c_3x^3 + c_2x^2 + c_1x^1 + c_0
            return (((((c5 * x + c4) * x + c3) * x + c2) * x + c1) * x + c0);
         }
      };

      template <typename Type>
      struct poly_impl <Type,4>
      {
         static inline T evaluate(const Type x, const Type c4, const Type c3, const Type c2, const Type c1, const Type c0)
         {
            //p(x) = c_4x^4 + c_3x^3 + c_2x^2 + c_1x^1 + c_0
            return ((((c4 * x + c3) * x + c2) * x + c1) * x + c0);
         }
      };

      template <typename Type>
      struct poly_impl <Type,3>
      {
         static inline T evaluate(const Type x, const Type c3, const Type c2, const Type c1, const Type c0)
         {
            //p(x) = c_3x^3 + c_2x^2 + c_1x^1 + c_0
            return (((c3 * x + c2) * x + c1) * x + c0);
         }
      };

      template <typename Type>
      struct poly_impl <Type,2>
      {
         static inline T evaluate(const Type x, const Type c2, const Type c1, const Type c0)
         {
            //p(x) = c_2x^2 + c_1x^1 + c_0
            return ((c2 * x + c1) * x + c0);
         }
      };

      template <typename Type>
      struct poly_impl <Type,1>
      {
         static inline T evaluate(const Type x, const Type c1, const Type c0)
         {
            //p(x) = c_1x^1 + c_0
            return (c1 * x + c0);
         }
      };

   public:

      polynomial() : exprtk::ifunction<T>((N+2 <= 20) ? (N + 2) : std::numeric_limits<std::size_t>::max()) {}

      inline virtual T operator()(const T& x, const T& c1, const T& c0)
      {
         return ((1 == N) ? poly_impl<T,1>::evaluate(x,c1,c0) : std::numeric_limits<T>::quiet_NaN());
      }

      inline virtual T operator()(const T& x, const T& c2, const T& c1, const T& c0)
      {
         return ((2 == N) ? poly_impl<T,2>::evaluate(x,c2,c1,c0) : std::numeric_limits<T>::quiet_NaN());
      }

      inline virtual T operator()(const T& x, const T& c3, const T& c2, const T& c1, const T& c0)
      {
         return ((3 == N) ? poly_impl<T,3>::evaluate(x,c3,c2,c1,c0) : std::numeric_limits<T>::quiet_NaN());
      }

      inline virtual T operator()(const T& x, const T& c4, const T& c3, const T& c2, const T& c1, const T& c0)
      {
         return ((4 == N) ? poly_impl<T,4>::evaluate(x,c4,c3,c2,c1,c0) : std::numeric_limits<T>::quiet_NaN());
      }

      inline virtual T operator()(const T& x, const T& c5, const T& c4, const T& c3, const T& c2, const T& c1, const T& c0)
      {
         return ((5 == N) ? poly_impl<T,5>::evaluate(x,c5,c4,c3,c2,c1,c0) : std::numeric_limits<T>::quiet_NaN());
      }

      inline virtual T operator()(const T& x, const T& c6, const T& c5, const T& c4, const T& c3, const T& c2, const T& c1, const T& c0)
      {
         return ((6 == N) ? poly_impl<T,6>::evaluate(x,c6,c5,c4,c3,c2,c1,c0) : std::numeric_limits<T>::quiet_NaN());
      }

      inline virtual T operator()(const T& x, const T& c7, const T& c6, const T& c5, const T& c4, const T& c3, const T& c2, const T& c1, const T& c0)
      {
         return ((7 == N) ? poly_impl<T,7>::evaluate(x,c7,c6,c5,c4,c3,c2,c1,c0) : std::numeric_limits<T>::quiet_NaN());
      }

      inline virtual T operator()(const T& x, const T& c8, const T& c7, const T& c6, const T& c5, const T& c4, const T& c3, const T& c2, const T& c1, const T& c0)
      {
         return ((8 == N) ? poly_impl<T,8>::evaluate(x,c8,c7,c6,c5,c4,c3,c2,c1,c0) : std::numeric_limits<T>::quiet_NaN());
      }

      inline virtual T operator()(const T& x, const T& c9, const T& c8, const T& c7, const T& c6, const T& c5, const T& c4, const T& c3, const T& c2, const T& c1, const T& c0)
      {
         return ((9 == N) ? poly_impl<T,9>::evaluate(x,c9,c8,c7,c6,c5,c4,c3,c2,c1,c0) : std::numeric_limits<T>::quiet_NaN());
      }

      inline virtual T operator()(const T& x, const T& c10, const T& c9, const T& c8, const T& c7, const T& c6, const T& c5, const T& c4, const T& c3, const T& c2, const T& c1, const T& c0)
      {
         return ((10 == N) ? poly_impl<T,10>::evaluate(x,c10,c9,c8,c7,c6,c5,c4,c3,c2,c1,c0) : std::numeric_limits<T>::quiet_NaN());
      }

      inline virtual T operator()()
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

      inline virtual T operator()(const T&, const T&)
      {
         return std::numeric_limits<T>::quiet_NaN();
      }

   };

   template <typename T>
   inline bool pgo_primer()
   {
      static const std::string expression_list[]
                                        = {
                                             "(y + x)",
                                             "2 * (y + x)",
                                             "(2 * y + 2 * x)",
                                             "(y + x / y) * (x - y / x)",
                                             "x / ((x + y) * (x - y)) / y",
                                             "1 - ((x * y) + (y / x)) - 3",
                                             "sin(2 * x) + cos(pi / y)",
                                             "1 - sin(2 * x) + cos(pi / y)",
                                             "sqrt(1 - sin(2 * x) + cos(pi / y) / 3)",
                                             "(x^2 / sin(2 * pi / y)) -x / 2",
                                             "x + (cos(y - sin(2 / x * pi)) - sin(x - cos(2 * y / pi))) - y",
                                             "clamp(-1.0, sin(2 * pi * x) + cos(y / 2 * pi), +1.0)",
                                             "max(3.33, min(sqrt(1 - sin(2 * x) + cos(pi / y) / 3), 1.11))",
                                             "if(avg(x,y) <= x + y, x - y, x * y) + 2 * pi / x",
                                             "1.1x^1 + 2.2y^2 - 3.3x^3 + 4.4y^4 - 5.5x^5 + 6.6y^6 - 7.7x^27 + 8.8y^55",
                                             "(yy + xx)",
                                             "2 * (yy + xx)",
                                             "(2 * yy + 2 * xx)",
                                             "(yy + xx / yy) * (xx - yy / xx)",
                                             "xx / ((xx + yy) * (xx - yy)) / yy",
                                             "1 - ((xx * yy) + (yy / xx)) - 3",
                                             "sin(2 * xx) + cos(pi / yy)",
                                             "1 - sin(2 * xx) + cos(pi / yy)",
                                             "sqrt(1 - sin(2 * xx) + cos(pi / yy) / 3)",
                                             "(xx^2 / sin(2 * pi / yy)) -xx / 2",
                                             "xx + (cos(yy - sin(2 / xx * pi)) - sin(xx - cos(2 * yy / pi))) - yy",
                                             "clamp(-1.0, sin(2 * pi * xx) + cos(yy / 2 * pi), +1.0)",
                                             "max(3.33, min(sqrt(1 - sin(2 * xx) + cos(pi / yy) / 3), 1.11))",
                                             "if(avg(xx,yy) <= xx + yy, xx - yy, xx * yy) + 2 * pi / xx",
                                             "1.1xx^1 + 2.2yy^2 - 3.3xx^3 + 4.4yy^4 - 5.5xx^5 + 6.6yy^6 - 7.7xx^27 + 8.8yy^55"
                                          };
      static const std::size_t expression_list_size = sizeof(expression_list) / sizeof(std::string);

      T  x = T(0);
      T  y = T(0);
      T xx = T(0);
      T yy = T(0);

      exprtk::symbol_table<T> symbol_table;
      symbol_table.add_constants();
      symbol_table.add_variable( "x", x);
      symbol_table.add_variable( "y", y);
      symbol_table.add_variable("xx",xx);
      symbol_table.add_variable("yy",yy);

      typedef typename std::deque<exprtk::expression<T> > expr_list_t;
      expr_list_t optimized_expr_list;
      expr_list_t unoptimized_expr_list;

      const std::size_t rounds = 1000;

      //Generate optimised expressions
      {
         for (std::size_t r = 0; r < rounds; ++r)
         {
            optimized_expr_list.clear();
            exprtk::parser<T> parser;
            for (std::size_t i = 0; i < expression_list_size; ++i)
            {
               exprtk::expression<T> expression;
               expression.register_symbol_table(symbol_table);
               if (!parser.compile(expression_list[i],expression,exprtk::parser<T>::e_all))
               {
                  return false;
               }
               optimized_expr_list.push_back(expression);
            }
         }
      }

      //Generate unoptimised expressions
      {
         for (std::size_t r = 0; r < rounds; ++r)
         {
            unoptimized_expr_list.clear();
            exprtk::parser<T> parser;
            for (std::size_t i = 0; i < expression_list_size; ++i)
            {
               exprtk::expression<T> expression;
               expression.register_symbol_table(symbol_table);
               if (!parser.compile(expression_list[i],expression,exprtk::parser<T>::e_none))
               {
                  return false;
               }
               unoptimized_expr_list.push_back(expression);
            }
         }
      }

      struct execute
      {
         static inline T process(T& x, T& y, expression<T>& expression)
         {
            static const T lower_bound = T(-20.0);
            static const T upper_bound = T(+20.0);
            T delta = T(0.1);
            T total = T(0.0);
            for (x = lower_bound; x <= upper_bound; x += delta)
            {
               for (y = lower_bound; y <= upper_bound; y += delta)
               {
                  total += expression.value();
               }
            }
            return total;
         }
      };
      for (std::size_t i = 0; i < optimized_expr_list.size(); ++i)
      {
         execute::process( x, y,  optimized_expr_list[i]);
         execute::process(xx,yy,  optimized_expr_list[i]);
         execute::process( x, y,unoptimized_expr_list[i]);
         execute::process(xx,yy,unoptimized_expr_list[i]);
      }

      {
         for (std::size_t i = 0; i < 10000; ++i)
         {
            T v = T(123.456 + i);
                 if (details::numeric::nequal(details::numeric::fast_exp<T, 1>::result(v),std::pow(v,T( 1.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T, 2>::result(v),std::pow(v,T( 2.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T, 3>::result(v),std::pow(v,T( 3.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T, 4>::result(v),std::pow(v,T( 4.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T, 5>::result(v),std::pow(v,T( 5.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T, 6>::result(v),std::pow(v,T( 6.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T, 7>::result(v),std::pow(v,T( 7.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T, 8>::result(v),std::pow(v,T( 8.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T, 9>::result(v),std::pow(v,T( 9.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,10>::result(v),std::pow(v,T(10.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,11>::result(v),std::pow(v,T(11.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,12>::result(v),std::pow(v,T(12.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,13>::result(v),std::pow(v,T(13.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,14>::result(v),std::pow(v,T(14.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,15>::result(v),std::pow(v,T(15.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,16>::result(v),std::pow(v,T(16.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,17>::result(v),std::pow(v,T(17.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,18>::result(v),std::pow(v,T(18.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,19>::result(v),std::pow(v,T(19.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,20>::result(v),std::pow(v,T(20.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,21>::result(v),std::pow(v,T(21.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,22>::result(v),std::pow(v,T(22.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,23>::result(v),std::pow(v,T(23.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,24>::result(v),std::pow(v,T(24.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,25>::result(v),std::pow(v,T(25.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,26>::result(v),std::pow(v,T(26.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,27>::result(v),std::pow(v,T(27.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,28>::result(v),std::pow(v,T(28.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,29>::result(v),std::pow(v,T(29.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,30>::result(v),std::pow(v,T(30.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,31>::result(v),std::pow(v,T(31.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,32>::result(v),std::pow(v,T(32.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,33>::result(v),std::pow(v,T(33.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,34>::result(v),std::pow(v,T(34.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,35>::result(v),std::pow(v,T(35.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,36>::result(v),std::pow(v,T(36.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,37>::result(v),std::pow(v,T(37.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,38>::result(v),std::pow(v,T(38.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,39>::result(v),std::pow(v,T(39.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,40>::result(v),std::pow(v,T(40.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,41>::result(v),std::pow(v,T(41.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,42>::result(v),std::pow(v,T(42.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,43>::result(v),std::pow(v,T(43.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,44>::result(v),std::pow(v,T(44.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,45>::result(v),std::pow(v,T(45.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,46>::result(v),std::pow(v,T(46.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,47>::result(v),std::pow(v,T(47.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,48>::result(v),std::pow(v,T(48.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,49>::result(v),std::pow(v,T(49.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,50>::result(v),std::pow(v,T(50.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,51>::result(v),std::pow(v,T(51.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,52>::result(v),std::pow(v,T(52.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,53>::result(v),std::pow(v,T(53.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,54>::result(v),std::pow(v,T(54.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,55>::result(v),std::pow(v,T(55.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,56>::result(v),std::pow(v,T(56.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,57>::result(v),std::pow(v,T(57.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,58>::result(v),std::pow(v,T(58.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,59>::result(v),std::pow(v,T(59.0)))) return false;
            else if (details::numeric::nequal(details::numeric::fast_exp<T,60>::result(v),std::pow(v,T(60.0)))) return false;
            else
               return true;
         }
      }
      return true;
   }

}

#ifdef WIN32
   #ifndef NOMINMAX
      #define NOMINMAX
   #endif
   #ifndef WIN32_LEAN_AND_MEAN
      #define WIN32_LEAN_AND_MEAN
   #endif
   #include <windows.h>
#else
   #include <sys/time.h>
   #include <sys/types.h>
#endif

namespace exprtk
{

   class timer
   {
   public:

      #ifdef WIN32
         timer()
         : in_use_(false)
         {
            QueryPerformanceFrequency(&clock_frequency_);
         }

         inline void start()
         {
            in_use_ = true;
            QueryPerformanceCounter(&start_time_);
         }

         inline void stop()
         {
            QueryPerformanceCounter(&stop_time_);
            in_use_ = false;
         }

         inline double time() const
         {
            return (1.0 * (stop_time_.QuadPart - start_time_.QuadPart)) / (1.0 * clock_frequency_.QuadPart);
         }

      #else

         timer()
         : in_use_(false)
         {
            start_time_.tv_sec  = 0;
            start_time_.tv_usec = 0;
            stop_time_.tv_sec   = 0;
            stop_time_.tv_usec  = 0;
         }

         inline void start()
         {
            in_use_ = true;
            gettimeofday(&start_time_,0);
         }

         inline void stop()
         {
            gettimeofday(&stop_time_, 0);
            in_use_ = false;
         }

         inline unsigned long long int usec_time() const
         {
            if (!in_use_)
            {
               if (stop_time_.tv_sec >= start_time_.tv_sec)
               {
                  return 1000000 * (stop_time_.tv_sec  - start_time_.tv_sec ) +
                                   (stop_time_.tv_usec - start_time_.tv_usec);
               }
               else
                  return std::numeric_limits<unsigned long long int>::max();
            }
            else
               return std::numeric_limits<unsigned long long int>::max();
         }

         inline double time() const
         {
            return usec_time() * 0.000001;
         }

      #endif

         inline bool in_use() const
         {
            return in_use_;
         }

   private:

         bool in_use_;

      #ifdef WIN32
         LARGE_INTEGER start_time_;
         LARGE_INTEGER stop_time_;
         LARGE_INTEGER clock_frequency_;
      #else
         struct timeval start_time_;
         struct timeval stop_time_;
      #endif
   };

   namespace information
   {
      static const char* library = "Mathematical Expression Toolkit";
      static const char* version = "2.71828182845904523536028";
      static const char* date    = "20120505";

      static inline std::string data()
      {
         static const std::string info_str = std::string(library) +
                                             std::string(" v") + std::string(version) +
                                             std::string(" (") + date + std::string(")");
         return info_str;
      }

   } // namespace information

} // namespace exprtk

#endif
