/exprtk.hpp

Large files files are truncated, but you can click here to view the full file

/*
 ******************************************************************
 *           C++ Mathematical Expression Toolkit Library          *
 *                                                                *
 * Author: Arash Partow (1999-2015)                               *
 * 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) (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) (2sin(x)cos(2y)7 + 1) == (2 * sin(x) * cos(2*y) * 7 + 1)  *
 * (12) (x ilike 's*ri?g') and [y < (3 z^7 + w)]                  *
 *                                                                *
 ******************************************************************
*/


#ifndef INCLUDE_EXPRTK_HPP
#define INCLUDE_EXPRTK_HPP


#include <algorithm>
#include <cctype>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <deque>
#include <exception>
#include <functional>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <set>
#include <stack>
#include <stdexcept>
#include <string>
#include <utility>
#include <vector>


namespace exprtk
{
   #if exprtk_enable_debugging
     #define exprtk_debug(params) printf params
   #else
     #define exprtk_debug(params) (void)0
   #endif

   namespace details
   {
      inline bool is_whitespace(const char c)
      {
         return (' '  == c) || ('\n' == c) ||
                ('\r' == c) || ('\t' == c) ||
                ('\b' == c) || ('\v' == c) ||
                ('\f' == 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) || ('&' == 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_letter_or_digit(const char c)
      {
         return is_letter(c) || is_digit(c);
      }

      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_bracket(const char c)
      {
         return is_left_bracket(c) || is_right_bracket(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)          &&
                ('\'' != 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;
      }

      inline bool is_valid_sf_symbol(const std::string& symbol)
      {
         // Special function: $f12 or $F34
         return (4 == symbol.size())  &&
                ('$' == symbol[0])    &&
                imatch('f',symbol[1]) &&
                is_digit(symbol[2])   &&
                is_digit(symbol[3]);
      }

      inline const char& front(const std::string& s)
      {
         return s[0];
      }

      inline const char& back(const std::string& s)
      {
         return s[s.size() - 1];
      }

      inline std::string to_str(int i)
      {
         if (0 == i)
            return std::string("0");

         std::string result;

         if (i < 0)
         {
            for ( ; i; i /= 10)
            {
               result += '0' + char(-(i % 10));
            }

            result += '-';
         }
         else
         {
            for ( ; i; i /= 10)
            {
               result += '0' + char(i % 10);
            }
         }

         std::reverse(result.begin(), result.end());

         return result;
      }

      inline bool is_hex_digit(const std::string::value_type digit)
      {
         return (('0' <= digit) && (digit <= '9')) ||
                (('A' <= digit) && (digit <= 'F')) ||
                (('a' <= digit) && (digit <= 'f')) ;
      }

      inline unsigned char hex_to_bin(unsigned char h)
      {
         if (('0' <= h) && (h <= '9'))
            return (h - '0');
         else
            return (std::toupper(h) - 'A');
      }

      template <typename Iterator>
      inline void parse_hex(Iterator& itr, Iterator end, std::string::value_type& result)
      {
         if (
              (end !=  (itr    )) &&
              (end !=  (itr + 1)) &&
              (end !=  (itr + 2)) &&
              (end !=  (itr + 3)) &&
              ('0' == *(itr    )) &&
              (
                ('x' == *(itr + 1)) ||
                ('X' == *(itr + 1))
              ) &&
              (is_hex_digit(*(itr + 2))) &&
              (is_hex_digit(*(itr + 3)))
            )
         {
            result = hex_to_bin(*(itr + 2)) << 4 | hex_to_bin(*(itr + 3));
            itr += 3;
         }
         else
            result = '\0';
      }

      inline void cleanup_escapes(std::string& s)
      {
         typedef std::string::iterator str_itr_t;

         str_itr_t itr1 = s.begin();
         str_itr_t itr2 = s.begin();
         str_itr_t end  = s.end  ();

         std::size_t removal_count  = 0;

         while (end != itr1)
         {
            if ('\\' == (*itr1))
            {
               ++removal_count;

               if (end == ++itr1)
                  break;
               else if ('\\' != (*itr1))
               {
                  switch (*itr1)
                  {
                     case 'n' : (*itr1) = '\n'; break;
                     case 'r' : (*itr1) = '\r'; break;
                     case 't' : (*itr1) = '\t'; break;
                     case '0' : parse_hex(itr1, end, (*itr1));
                                removal_count += 3;
                                break;
                  }

                  continue;
               }
            }

            if (itr1 != itr2)
            {
               (*itr2) = (*itr1);
            }

            ++itr1;
            ++itr2;
         }

         s.resize(s.size() - removal_count);
      }

      class build_string
      {
      public:

         build_string(const std::size_t& initial_size = 64)
         {
            data_.reserve(initial_size);
         }

         inline build_string& operator << (const std::string& s)
         {
            data_ += s;
            return (*this);
         }

         inline build_string& operator << (const char* s)
         {
            data_ += std::string(s);
            return (*this);
         }

         inline operator std::string () const
         {
            return data_;
         }

         inline std::string as_string() const
         {
            return data_;
         }

      private:

         std::string data_;
      };

      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)
            {
               const char c1 = static_cast<char>(std::tolower(s1[i]));
               const char c2 = static_cast<char>(std::tolower(s2[i]));

               if (c1 > c2)
                  return false;
               else if (c1 < c2)
                  return true;
            }

            return s1.size() < s2.size();
         }
      };

      static const std::string reserved_words[] =
                                  {
                                    "break",  "case",  "continue",  "default",  "false",  "for",
                                    "if", "else", "ilike",  "in", "like", "and",  "nand", "nor",
                                    "not",  "null",  "or",   "repeat", "return",  "shl",  "shr",
                                    "swap", "switch", "true",  "until", "var",  "while", "xnor",
                                    "xor", "&", "|"
                                  };

      static const std::size_t reserved_words_size = sizeof(reserved_words) / sizeof(std::string);

      static const std::string reserved_symbols[] =
                                  {
                                    "abs",  "acos",  "acosh",  "and",  "asin",  "asinh", "atan",
                                    "atanh", "atan2", "avg",  "break", "case", "ceil",  "clamp",
                                    "continue",   "cos",   "cosh",   "cot",   "csc",  "default",
                                    "deg2grad",  "deg2rad",   "equal",  "erf",   "erfc",  "exp",
                                    "expm1",  "false",   "floor",  "for",   "frac",  "grad2deg",
                                    "hypot", "iclamp", "if",  "else", "ilike", "in",  "inrange",
                                    "like",  "log",  "log10", "log2",  "logn",  "log1p", "mand",
                                    "max", "min",  "mod", "mor",  "mul", "ncdf",  "nand", "nor",
                                    "not",   "not_equal",   "null",   "or",   "pow",  "rad2deg",
                                    "repeat", "return", "root", "round", "roundn", "sec", "sgn",
                                    "shl", "shr", "sin", "sinc", "sinh", "sqrt",  "sum", "swap",
                                    "switch", "tan",  "tanh", "true",  "trunc", "until",  "var",
                                    "while", "xnor", "xor", "&", "|"
                                  };

      static const std::size_t reserved_symbols_size = sizeof(reserved_symbols) / sizeof(std::string);

      static const std::string base_function_list[] =
                                  {
                                    "abs", "acos",  "acosh", "asin",  "asinh", "atan",  "atanh",
                                    "atan2",  "avg",  "ceil",  "clamp",  "cos",  "cosh",  "cot",
                                    "csc",  "equal",  "erf",  "erfc",  "exp",  "expm1", "floor",
                                    "frac", "hypot", "iclamp",  "like", "log", "log10",  "log2",
                                    "logn", "log1p", "mand", "max", "min", "mod", "mor",  "mul",
                                    "ncdf",  "pow",  "root",  "round",  "roundn",  "sec", "sgn",
                                    "sin", "sinc", "sinh", "sqrt", "sum", "swap", "tan", "tanh",
                                    "trunc",  "not_equal",  "inrange",  "deg2grad",   "deg2rad",
                                    "rad2deg", "grad2deg"
                                  };

      static const std::size_t base_function_list_size = sizeof(base_function_list) / sizeof(std::string);

      static const std::string logic_ops_list[] =
                                  {
                                    "and", "nand", "nor", "not", "or",  "xnor", "xor", "&", "|"
                                  };

      static const std::size_t logic_ops_list_size = sizeof(logic_ops_list) / sizeof(std::string);

      static const std::string cntrl_struct_list[] =
                                  {
                                    "for", "if", "repeat", "switch", "while"
                                  };

      static const std::size_t cntrl_struct_list_size = sizeof(cntrl_struct_list) / 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;
      }

      inline bool is_base_function(const std::string& function_name)
      {
         for (std::size_t i = 0; i < base_function_list_size; ++i)
         {
            if (imatch(function_name,base_function_list[i]))
            {
               return true;
            }
         }

         return false;
      }

      inline bool is_control_struct(const std::string& cntrl_strct)
      {
         for (std::size_t i = 0; i < cntrl_struct_list_size; ++i)
         {
            if (imatch(cntrl_strct,cntrl_struct_list[i]))
            {
               return true;
            }
         }

         return false;
      }

      inline bool is_logic_opr(const std::string& lgc_opr)
      {
         for (std::size_t i = 0; i < cntrl_struct_list_size; ++i)
         {
            if (imatch(lgc_opr,logic_ops_list[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(),
                                                  '*',
                                                  '?');
      }

      inline bool sequence_match(const std::string& pattern,
                                 const std::string& str,
                                 std::size_t&       diff_index,
                                 char&              diff_value)
      {
         if (str.empty() || pattern.empty())
            return false;
         else if ('*' == pattern[0])
            return false;

         typedef std::string::const_iterator itr_t;

         itr_t p_itr = pattern.begin();
         itr_t s_itr = str    .begin();

         itr_t p_end = pattern.end();
         itr_t s_end = str    .end();

         while ((s_end != s_itr) && (p_end != p_itr))
         {
            if ('*' == (*p_itr))
            {
               const char target = std::toupper(*(p_itr - 1));

               if ('*' == target)
               {
                  diff_index = std::distance(str.begin(),s_itr);
                  diff_value = std::toupper(*p_itr);

                  return false;
               }
               else
                  ++p_itr;

               while (s_itr != s_end)
               {
                  if (target != std::toupper(*s_itr))
                     break;
                  else
                     ++s_itr;
               }

               continue;
            }
            else if (
                      ('?' != *p_itr) &&
                      std::toupper(*p_itr) != std::toupper(*s_itr)
                    )
            {
               diff_index = std::distance(str.begin(),s_itr);
               diff_value = std::toupper(*p_itr);

               return false;
            }

            ++p_itr;
            ++s_itr;
         }

         return (
                  (s_end == s_itr) &&
                  (
                    (p_end ==  p_itr) ||
                    ('*'   == *p_itr)
                  )
                );
      }

      static const double pow10[] = {
                                      1.0,
                                      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
                                    };

     static const std::size_t pow10_size = sizeof(pow10) / sizeof(double);

      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;
            static const double log2    =  0.693147180559945309417;
            static const double sqrt2   =  1.414213562373095048801;
         }

         namespace details
         {
            struct unknown_type_tag {};
            struct real_type_tag    {};
            struct complex_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_complex_type_tag(T)     \
            template<> struct number_type<std::complex<T> > \
            { typedef complex_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_complex_type_tag(double     )
            exprtk_register_complex_type_tag(long double)
            exprtk_register_complex_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>
            struct epsilon_type
            {
               static inline T value()
               {
                  const T epsilon = T(0.0000000001);
                  return epsilon;
               }
            };

            template <>
            struct epsilon_type <float>
            {
               static inline float value()
               {
                  const float epsilon = float(0.000001f);
                  return epsilon;
               }
            };

            template <>
            struct epsilon_type <long double>
            {
               static inline long double value()
               {
                  const long double epsilon = (long double)(0.000000000001);
                  return epsilon;
               }
            };

            template <typename T>
            inline bool is_nan_impl(const T v, real_type_tag)
            {
               return std::not_equal_to<T>()(v,v);
            }

            template <typename T>
            inline int to_int32_impl(const T v, real_type_tag)
            {
               return static_cast<int>(v);
            }

            template <typename T>
            inline long long int to_int64_impl(const T v, real_type_tag)
            {
               return static_cast<long long int>(v);
            }

            template <typename T>
            inline bool is_true_impl(const T v)
            {
               return std::not_equal_to<T>()(T(0),v);
            }

            template <typename T>
            inline bool is_false_impl(const T v)
            {
               return std::equal_to<T>()(T(0),v);
            }

            template <typename T>
            inline T abs_impl(const T v, real_type_tag)
            {
               return ((v >= T(0)) ? v : -v);
            }

            template <typename T>
            inline T min_impl(const T v0, const T v1, real_type_tag)
            {
               return std::min<T>(v0,v1);
            }

            template <typename T>
            inline T max_impl(const T v0, const T v1, real_type_tag)
            {
               return std::max<T>(v0,v1);
            }

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

            inline float equal_impl(const float v0, const float v1, real_type_tag)
            {
               const float epsilon = epsilon_type<float>::value();
               return (abs_impl(v0 - v1,real_type_tag()) <= (std::max(1.0f,std::max(abs_impl(v0,real_type_tag()),abs_impl(v1,real_type_tag()))) * epsilon)) ? 1.0f : 0.0f;
            }

            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 expm1_impl(const T v, real_type_tag)
            {
               // return std::expm1<T>(v);
               if (abs_impl(v,real_type_tag()) < T(0.00001))
                  return v + (T(0.5) * v * v);
               else
                  return std::exp(v) - T(1);
            }

            template <typename T>
            inline T expm1_impl(const T v, int_type_tag)
            {
               return T(std::exp<double>(v)) - T(1);
            }

            template <typename T>
            inline T nequal_impl(const T v0, const T v1, real_type_tag)
            {
               typedef real_type_tag rtg;
               const T epsilon = epsilon_type<T>::value();
               return (abs_impl(v0 - v1,rtg()) > (std::max(T(1),std::max(abs_impl(v0,rtg()),abs_impl(v1,rtg()))) * epsilon)) ? T(1) : T(0);
            }

            inline float nequal_impl(const float v0, const float v1, real_type_tag)
            {
               typedef real_type_tag rtg;
               const float epsilon = epsilon_type<float>::value();
               return (abs_impl(v0 - v1,rtg()) > (std::max(1.0f,std::max(abs_impl(v0,rtg()),abs_impl(v1,rtg()))) * epsilon)) ? 1.0f : 0.0f;
            }

            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 log1p_impl(const T v, real_type_tag)
            {
               if (v > T(-1))
               {
                  if (abs_impl(v,real_type_tag()) > T(0.0001))
                  {
                     return std::log(T(1) + v);
                  }
                  else
                     return (T(-0.5) * v + T(1)) * v;
               }
               else
                  return std::numeric_limits<T>::quiet_NaN();
            }

            template <typename T>
            inline T log1p_impl(const T v, int_type_tag)
            {
               if (v > T(-1))
               {
                  return std::log(T(1) + v);
               }
               else
                  return std::numeric_limits<T>::quiet_NaN();
            }

            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 round_impl(const T v, real_type_tag)
            {
               return ((v < T(0)) ? std::ceil(v - T(0.5)) : std::floor(v + T(0.5)));
            }

            template <typename T>
            inline T roundn_impl(const T v0, const T v1, real_type_tag)
            {
               const int index = std::max<int>(0, std::min<int>(pow10_size - 1, (int)std::floor(v1)));
               const T p10 = T(pow10[index]);
               if (v0 < T(0))
                  return T(std::ceil ((v0 * p10) - T(0.5)) / p10);
               else
                  return T(std::floor((v0 * p10) + T(0.5)) / p10);
            }

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

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

            template <typename T>
            inline T hypot_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)) return T(+1);
               else if (v < T(0)) return T(-1);
               else               return T( 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 and_impl(const T v0, const T v1, real_type_tag)
            {
               return (is_true_impl(v0) && is_true_impl(v1)) ? T(1) : T(0);
            }

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

            template <typename T>
            inline T nand_impl(const T v0, const T v1, real_type_tag)
            {
               return (is_false_impl(v0) || is_false_impl(v1)) ? T(1) : T(0);
            }

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

            template <typename T>
            inline T or_impl(const T v0, const T v1, real_type_tag)
            {
               return (is_true_impl(v0) || is_true_impl(v1)) ? T(1) : T(0);
            }

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

            template <typename T>
            inline T nor_impl(const T v0, const T v1, real_type_tag)
            {
               return (is_false_impl(v0) && is_false_impl(v1)) ? T(1) : T(0);
            }

            template <typename T>
            inline T nor_impl(const T v0, const T v1, int_type_tag)
            {
               return !(v0 || v1);
            }

            template <typename T>
            inline T xor_impl(const T v0, const T v1, real_type_tag)
            {
               return (is_false_impl(v0) != is_false_impl(v1)) ? T(1) : T(0);
            }

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

            template <typename T>
            inline T xnor_impl(const T v0, const T v1, real_type_tag)
            {
               const bool v0_true = is_true_impl(v0);
               const bool v1_true = is_true_impl(v1);
               if ((v0_true &&  v1_true) || (!v0_true && !v1_true))
                  return T(1);
               else
                  return T(0);
            }

            template <typename T>
            inline T xnor_impl(const T v0, const T v1, int_type_tag)
            {
               const bool v0_true = is_true_impl(v0);
               const bool v1_true = is_true_impl(v1);
               if ((v0_true &&  v1_true) || (!v0_true && !v1_true))
                  return T(1);
               else
                  return T(0);
            }

            template <typename T>
            inline T erf_impl(T v, real_type_tag)
            {
               #if defined(_WIN32) || defined(__WIN32__) || defined(WIN32)
               // Credits: Abramowitz & Stegun Equations 7.1.25-28
               const T t = T(1) / (T(1) + T(0.5) * abs_impl(v,real_type_tag()));
               static const T c[] = {
                                      T( 1.26551223), T(1.00002368),
                                      T( 0.37409196), T(0.09678418),
                                      T(-0.18628806), T(0.27886807),
                                      T(-1.13520398), T(1.48851587),
                                      T(-0.82215223), T(0.17087277)
                                    };
               T result = T(1) - t * std::exp((-v * v) -
                                      c[0] + t * (c[1] + t *
                                     (c[2] + t * (c[3] + t *
                                     (c[4] + t * (c[5] + t *
                                     (c[6] + t * (c[7] + t *
                                     (c[8] + t * (c[9]))))))))));
               return (v >= T(0)) ? result : -result;
               #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) - 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 ncdf_impl(T v, real_type_tag)
            {
               T cnd = T(0.5) * (T(1) + erf_impl(
                                           abs_impl(v,real_type_tag()) /
                                           T(numeric::constant::sqrt2),real_type_tag()));
               return  (v < T(0)) ? (T(1) - cnd) : cnd;
            }

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

            template <typename T>
            inline T sinc_impl(T v, real_type_tag)
            {
               if (std::abs(v) >= std::numeric_limits<T>::epsilon())
                   return(std::sin(v) / v);
               else
                  return T(1);
            }

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

            template <typename T> inline T  acos_impl(const T v, real_type_tag) { return std::acos (v); }
            template <typename T> inline T acosh_impl(const T v, real_type_tag) { return std::log(v + std::sqrt((v * v) - T(1))); }
            template <typename T> inline T  asin_impl(const T v, real_type_tag) { return std::asin (v); }
            template <typename T> inline T asinh_impl(const T v, real_type_tag) { return std::log(v + std::sqrt((v * v) + T(1))); }
            template <typename T> inline T  atan_impl(const T v, real_type_tag) { return std::atan (v); }
            template <typename T> inline T atanh_impl(const T v, real_type_tag) { return (std::log(T(1) + v) - log(T(1) - v)) / T(2); }
            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  log2_impl(const T v, real_type_tag) { return std::log(v)/T(numeric::constant::log2); }
            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   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 (std::not_equal_to<T>()(T(0),v) ? T(0) : T(1)); }
            template <typename T> inline T  frac_impl(const T v, real_type_tag) { return (v - static_cast<long long>(v)); }
            template <typename T> inline T trunc_impl(const T v, real_type_tag) { return T(static_cast<long long>(v));    }

            template <typename T> inline T   abs_impl(const T v, int_type_tag) { return ((v >= T(0)) ? v : -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  log2_impl(const T v, int_type_tag) { return std::log(v)/T(numeric::constant::log2); }
            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  frac_impl(const T  , int_type_tag) { return T(0);          }
            template <typename T> inline T trunc_impl(const T v, int_type_tag) { return 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 acosh_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 asinh_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 atanh_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 std::equal_to<T>()(T(0),std::fmod(v,T(1)));
            }

            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 int to_int32(const T v)
         {
            typename details::number_type<T>::type num_type;
            return to_int32_impl(v,num_type);
         }

         template <typename T>
         inline long long int to_int64(const T v)
         {
            typename details::number_type<T>::type num_type;
            return to_int64_impl(v,num_type);
         }

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

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

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

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

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

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

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

         template <typename T>
     …