Как создать выражение калькулятора, которое может вычислять произвольное длинное выражение ?

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образец
pi = 3,14 радиус = 3 sin( pi / 2 ) + pi * радиус ^ 2 + 0x1F - 1100b
это даст ошибку из-за двоичных и шестнадцатеричных чисел.

Что я уже пробовал:

#include "parser.h"


// returns a number from 0 up to, but excluding x
const int getrandom (const int x)
{
	if (x <= 0)
		return 0;

	// r will be between 0 and 1 (but below 1 as we are dividing by RAND_MAX+1)
	double r = static_cast<double> (std::rand () % RAND_MAX) / (static_cast<double> (RAND_MAX) + 1.0);
	return floor (r * x);

}   // end of getrandom

const int roll (const int howmany, const int die)
{
	int count;
	int total = 0;

	for (count = 0; count < howmany; ++count)
		total += getrandom (die) + 1;

	return total;

} // end of roll


// returns true if a x% probability exists
// eg. percent (80) will be true 80% of the time


static int initRandom ()
  {
  srand   (time (NULL));
#ifndef WIN32
  srand48 (time (NULL));
#endif
  return 0;
  }

// initialise random number generator
static int someNumber = initRandom ();



// functions we can call from an expression

double DoInt (double arg)
  {
  return (double) arg;   // drop fractional part
  }
double toInteger(char c)
{
    if (c >= '0' && c <= '9') return c -'0';
    if (c >= 'a' && c <= 'f') return c -'a' + 0xa;
    if (c >= 'A' && c <= 'F') return c -'A' + 0xa;
    double noDigit = 0xf + 1;
    return noDigit;
}
double toHex(char c)
{
    return (std::tolower(c) == 'x' && toInteger(c) <= 0xf);
}
double DoRandom (double arg)
  {
  return getrandom (static_cast <double> (arg));  // random number in range 0 to arg
  }




const double DoIf (const double arg1, const double arg2, const double arg3)
  {
  if (arg1 != 0.0)
    return arg2;
  else
    return arg3;
  }
typedef double (*OneArgFunction)  (double arg);
typedef const double (*TwoArgFunction)  (const double arg1, const double arg2);
typedef const double (*ThreeArgFunction)  (const double arg1, const double arg2, const double arg3);

// maps of function names to functions
static std::map<std::string, OneArgFunction>    OneArgumentFunctions;
static std::map<std::string, TwoArgFunction>    TwoArgumentFunctions;
static std::map<std::string, ThreeArgFunction>  ThreeArgumentFunctions;

// for standard library functions
#define STD_FUNCTION(arg) OneArgumentFunctions [#arg] = arg

static int LoadOneArgumentFunctions ()
  {
  OneArgumentFunctions ["abs"] = fabs;
  STD_FUNCTION (acos);
  STD_FUNCTION (asin);
  STD_FUNCTION (atan);
#ifndef WIN32   // doesn't seem to exist under Visual C++ 6
  STD_FUNCTION (atanh);
#endif
  //STD_FUNCTION (ceil);
  STD_FUNCTION (cos);
  //STD_FUNCTION (cosh);
  STD_FUNCTION (exp);
  STD_FUNCTION (exp);
 // STD_FUNCTION (floor);
  STD_FUNCTION (log);
  STD_FUNCTION (log10);
  STD_FUNCTION (sin);
  //STD_FUNCTION (sinh);
  STD_FUNCTION (sqrt);
  STD_FUNCTION (tan);
  //STD_FUNCTION (tanh);

  OneArgumentFunctions ["int"] = DoInt;
  OneArgumentFunctions ["rand"] = DoRandom;
  OneArgumentFunctions ["rand"] = DoRandom;
 // OneArgumentFunctions ["percent"] = DoPercent;
  return 0;
  } // end of LoadOneArgumentFunctions


static int LoadThreeArgumentFunctions ()
  {
  ThreeArgumentFunctions ["if"]  = DoIf;
  return 0;
  } // end of LoadThreeArgumentFunctions

const Parser::TokenType Parser::GetToken (const bool ignoreSign)
  {
  word_.erase (0, std::string::npos);

  // skip spaces
  while (*pWord_ && isspace (*pWord_))
    ++pWord_;

  pWordStart_ = pWord_;   // remember where word_ starts *now*

  // look out for unterminated statements and things
  if (*pWord_ == 0 &&  // we have EOF
      type_ == END)  // after already detecting it
    throw std::runtime_error ("Unexpected end of expression.");

  unsigned char cFirstCharacter = *pWord_;        // first character in new word_

  if (cFirstCharacter == 0)    // stop at end of file
    {
    word_ = "<end of expression>";
    return type_ = END;
    }

  unsigned char cNextCharacter  = *(pWord_ + 1);  // 2nd character in new word_

  // look for number
  // can be: + or - followed by a decimal point
  // or: + or - followed by a digit
  // or: starting with a digit
  // or: decimal point followed by a digit
  if ((!ignoreSign &&
	   (cFirstCharacter == '+' || cFirstCharacter == '-') &&
	   (isdigit (cNextCharacter) || cNextCharacter == '.')
	   )
	  || isdigit (cFirstCharacter)
	  // allow decimal numbers without a leading 0. e.g. ".5"

	  || (cFirstCharacter == '.' && isdigit (cNextCharacter)) )
	  {
    // skip sign for now
    if ((cFirstCharacter == '+' || cFirstCharacter == '-'))
      pWord_++;
    while (isdigit (*pWord_) || *pWord_ == '.')
      pWord_++;

    // allow for 1.53158e+15
    if (*pWord_ == 'e' || *pWord_ == 'E')
      {
      pWord_++; // skip 'e'
      if ((*pWord_  == '+' || *pWord_  == '-'))
        pWord_++; // skip sign after e
      while (isdigit (*pWord_))  // now digits after e
        pWord_++;
      }

    word_ = std::string (pWordStart_, pWord_ - pWordStart_);

    std::istringstream is (word_);
    // parse std::string into double value
    is >> value_;

    if (is.fail () && !is.eof ())
      throw std::runtime_error ("Bad numeric literal: " + word_);
    return type_ = NUMBER;
    }   // end of number found

  // special test for 2-character sequences: <= >= == !=
  // also +=, -=, /=, *=
  if (cNextCharacter == '=')
    {
    switch (cFirstCharacter)
      {
      // comparisons
      case '=': type_ = EQ;   break;
      case '<': type_ = LE;   break;
      case '>': type_ = GE;   break;
      case '!': type_ = NE;   break;
      // assignments
      case '+': type_ = ASSIGN_ADD;   break;
      case '-': type_ = ASSIGN_SUB;   break;
      case '*': type_ = ASSIGN_MUL;   break;
      case '/': type_ = ASSIGN_DIV;   break;
      // none of the above
      default:  type_ = NONE; break;
      } // end of switch on cFirstCharacter

    if (type_ != NONE)
      {
      word_ = std::string (pWordStart_, 2);
      pWord_ += 2;   // skip both characters
      return type_;
      } // end of found one
    } // end of *=

  switch (cFirstCharacter)
    {
    case '&': if (cNextCharacter == '&')    // &&
                {
                word_ = std::string (pWordStart_, 2);
                pWord_ += 2;   // skip both characters
                return type_ = AND;
                }
              break;
   case '|': if (cNextCharacter == '|')   // ||
                {
                word_ = std::string (pWordStart_, 2);
                pWord_ += 2;   // skip both characters
                return type_ = OR;
                }
              break;
    // single-character symboles
    case '=':
    case '<':
    case '>':
    case '+':
    case '-':
    case '/':
    case '*':
    case '(':
    case ')':
    case ',':
    case '!':
      word_ = std::string (pWordStart_, 1);
      ++pWord_;   // skip it
      return type_ = TokenType (cFirstCharacter);
    } // end of switch on cFirstCharacter

  if (!isalpha (cFirstCharacter))
    {
    if (cFirstCharacter < ' ')
      {
      std::ostringstream s;
      s << "Unexpected character (decimal " << int (cFirstCharacter) << ")";
      throw std::runtime_error (s.str ());
      }
    else
      throw std::runtime_error ("Unexpected character: " + std::string (1, cFirstCharacter));
    }

  // we have a word (starting with A-Z) - pull it out
  while (isalnum (*pWord_) || *pWord_ == '_')
    ++pWord_;

  word_ = std::string (pWordStart_, pWord_ - pWordStart_);
  return type_ = NAME;
  }   // end of Parser::GetToken

// force load of functions at static initialisation time
static int doLoadOneArgumentFunctions = LoadOneArgumentFunctions ();
//static int doLoadTwoArgumentFunctions = LoadTwoArgumentFunctions ();
static int doLoadThreeArgumentFunctions = LoadThreeArgumentFunctions ();

const double Parser::Primary (const bool get)   // primary (base) tokens
  {

  if (get)
    GetToken ();    // one-token lookahead

  switch (type_)
    {
    case NUMBER:
      {
      double v = value_;
      GetToken (true);  // get next one (one-token lookahead)
      return v;
      }

         case 0xf :
        {
        if( type_==0xf){


         GetToken(true);
           return value_;
        }
        }
    case NAME:
      {
      std::string word = word_;
      GetToken (true);
      if (type_ == LHPAREN)
        {
        // might be single-argument function (eg. abs (x) )
        std::map<std::string, OneArgFunction>::const_iterator si;
        si = OneArgumentFunctions.find (word);
        if (si != OneArgumentFunctions.end ())
          {
          double v = Expression (true);   // get argument
          CheckToken (RHPAREN);
          GetToken (true);        // get next one (one-token lookahead)
          return si->second (v);  // evaluate function
          }

        // might be double-argument function (eg. roll (6, 2) )
        std::map<std::string, TwoArgFunction>::const_iterator di;
        di = TwoArgumentFunctions.find (word);
        if (di != TwoArgumentFunctions.end ())
          {
          double v1 = Expression (true);   // get argument 1 (not commalist)
          CheckToken (COMMA);
          double v2 = Expression (true);   // get argument 2 (not commalist)
          CheckToken (RHPAREN);
          GetToken (true);            // get next one (one-token lookahead)
          return di->second (v1, v2); // evaluate function
          }

       // might be double-argument function (eg. roll (6, 2) )
        std::map<std::string, ThreeArgFunction>::const_iterator ti;
        ti = ThreeArgumentFunctions.find (word);
        if (ti != ThreeArgumentFunctions.end ())
          {
          double v1 = Expression (true);   // get argument 1 (not commalist)
          CheckToken (COMMA);
          double v2 = Expression (true);   // get argument 2 (not commalist)
          CheckToken (COMMA);
          double v3 = Expression (true);   // get argument 3 (not commalist)
          CheckToken (RHPAREN);
          GetToken (true);  // get next one (one-token lookahead)
          return ti->second (v1, v2, v3); // evaluate function
          }

        throw std::runtime_error ("Function '" + word + "' not implemented.");
        }

      // not a function? must be a symbol in the symbol table
      double & v = symbols_ [word];  // get REFERENCE to symbol table entry
      // change table entry with expression? (eg. a = 22, or a = 22)
      switch (type_)
        {
        // maybe check for NaN or Inf here (see: isinf, isnan functions)
        case ASSIGN:     v  = Expression (true); break;
        case ASSIGN_ADD: v += Expression (true); break;
        case ASSIGN_SUB: v -= Expression (true); break;
        case ASSIGN_MUL: v *= Expression (true); break;
        case ASSIGN_DIV:
            {
            double d = Expression (true);
            if (d == 0.0)
              throw std::runtime_error ("Divide by zero");
            v /= d;
            break;   // change table entry with expression
            } // end of ASSIGN_DIV
        default: break;   // do nothing for others
        } // end of switch on type_
      return v;               // and return new value
      }

    case MINUS:               // unary minus
      return - Primary (true);

    case NOT:   // unary not
      return (Primary (true) == 0.0) ? 1.0 : 0.0;;

    case LHPAREN:
      {
      double v = CommaList (true);    // inside parens, you could have commas
      CheckToken (RHPAREN);
      GetToken (true);                // eat the )
      return v;
      }

    default:
      throw std::runtime_error ("Unexpected token: " + word_);

    } // end of switch on type

  } // end of Parser::Primary

const double Parser::Term (const bool get)    // multiply and divide
  {
  double left = Primary (get);
  while (true)
    {
    switch (type_)
      {
      case MULTIPLY:
        left *= Primary (true); break;
      case DIVIDE:
          {
          double d = Primary (true);
          if (d == 0.0)
            throw std::runtime_error ("Divide by zero");
          left /= d;
          break;
          }
      default:    return left;
      } // end of switch on type
    }   // end of loop
  } // end of Parser::Term

const double Parser::AddSubtract (const bool get)  // add and subtract
  {
  double left = Term (get);
  while (true)
    {
    switch (type_)
      {
      case PLUS:  left += Term (true); break;
      case MINUS: left -= Term (true); break;
      default:    return left;
      } // end of switch on type
    }   // end of loop
  } // end of Parser::AddSubtract

const double Parser::Comparison (const bool get)  // LT, GT, LE, EQ etc.
  {
  double left = AddSubtract (get);
  while (true)
    {
    switch (type_)
      {
      case LT:  left = left <  AddSubtract (true) ? 1.0 : 0.0; break;
      case GT:  left = left >  AddSubtract (true) ? 1.0 : 0.0; break;
      case LE:  left = left <= AddSubtract (true) ? 1.0 : 0.0; break;
      case GE:  left = left >= AddSubtract (true) ? 1.0 : 0.0; break;
      case EQ:  left = left == AddSubtract (true) ? 1.0 : 0.0; break;
      case NE:  left = left != AddSubtract (true) ? 1.0 : 0.0; break;
           default:    return left;
      } // end of switch on type
    }   // end of loop
  } // end of Parser::Comparison

const double Parser::Expression (const bool get)  // AND and OR
  {
  double left = Comparison (get);
  while (true)
    {
    switch (type_)
      {
      case AND:
            {
            double d = Comparison (true);   // don't want short-circuit evaluation
            left = (left != 0.0) && (d != 0.0);
            }
          break;
      case OR:
            {
            double d = Comparison (true);   // don't want short-circuit evaluation
            left = (left != 0.0) || (d != 0.0);
            }
          break;
      default:    return left;
      } // end of switch on type
    }   // end of loop
  } // end of Parser::Expression

const double Parser::CommaList (const bool get)  // expr1, expr2
  {
  double left = Expression (get);
  while (true)
    {
    switch (type_)
      {
      case COMMA:  left = Expression (true); break; // discard previous value
      default:    return left;
      } // end of switch on type
    }   // end of loop
  } // end of Parser::CommaList

const double Parser::Evaluate ()  // get result
  {
  pWord_    = program_.c_str ();
  type_     = NONE;
  double v = CommaList (true);
  if (type_ != END)
    throw std::runtime_error ("Unexpected text at end of expression: " + std::string (pWordStart_));
  return v;
  }

// change program and evaluate it
const double Parser::Evaluate (const std::string & program)  // get result
  {
  program_  = program;
  return Evaluate ();
  }

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