muparser.cpp

Mathematical expressions parser library

/*  
  Copyright (C) 2004, 2005 Ingo Berg

  Permission is hereby granted, free of charge, to any person obtaining a copy of this 
  software and associated documentation files (the "Software"), to deal in the Software
  without restriction, including without limitation the rights to use, copy, modify, 
  merge, publish, distribute, sublicense, and/or sell copies of the Software, and to 
  permit persons to whom the Software is furnished to do so, subject to the following conditions:

  The above copyright notice and this permission notice shall be included in all copies or 
  substantial portions of the Software.

  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT
  NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
  NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, 
  DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 
*/
#include "muParser.h"

#include <cmath>
#include <algorithm>
#include <numeric>

/** \brief Pi (what else?). */
#define PARSER_CONST_PI  3.141592653589793238462643

/** \brief The eulerian number. */
#define PARSER_CONST_E   2.718281828459045235360287

using namespace std;


/** \brief Namespace for mathematical applications. */
namespace mu
{

//---------------------------------------------------------------------------
// Trigonometric function
value_type Parser::Sin(value_type v)   { return sin(v);  }
value_type Parser::Cos(value_type v)   { return cos(v);  }
value_type Parser::Tan(value_type v)   { return tan(v);  }
value_type Parser::ASin(value_type v)  { return asin(v); }
value_type Parser::ACos(value_type v)  { return acos(v); }
value_type Parser::ATan(value_type v)  { return atan(v); }
value_type Parser::Sinh(value_type v)  { return sinh(v); }
value_type Parser::Cosh(value_type v)  { return cosh(v); }
value_type Parser::Tanh(value_type v)  { return tanh(v); }
value_type Parser::ASinh(value_type v) { return log(v + sqrt(v * v + 1)); }
value_type Parser::ACosh(value_type v) { return log(v + sqrt(v * v - 1)); }
value_type Parser::ATanh(value_type v) { return ((value_type)0.5 * log((1 + v) / (1 - v))); }

//---------------------------------------------------------------------------
// Logarithm functions
value_type Parser::Log2(value_type v)  { return log(v)/log((value_type)2); } // Logarithm base 2
value_type Parser::Log10(value_type v) { return log10(v); } // Logarithm base 10
value_type Parser::Ln(value_type v)    { return log(v);   } // Logarithm base e (natural logarithm)

//---------------------------------------------------------------------------
//  misc
value_type Parser::Exp(value_type v)   { return exp(v);   }
value_type Parser::Abs(value_type v)   { return fabs(v);  }
value_type Parser::Sqrt(value_type v)  { return sqrt(v);  }
value_type Parser::Rint(value_type v)  { return floor(v + (value_type)0.5); }
value_type Parser::Sign(value_type v)  { return (value_type)((v<0) ? -1 : (v>0) ? 1 : 0); }

//---------------------------------------------------------------------------
// Conditional (if then else)
value_type Parser::Ite(value_type v1, value_type v2, value_type v3) { return (v1==1) ? v2 : v3; }

//---------------------------------------------------------------------------
// Unary operator Callbacks: Infix operators
value_type Parser::UnaryMinus(value_type v) { return -v; }

//---------------------------------------------------------------------------
// Functions with variable number of arguments
// sum
value_type Parser::Sum(const value_type *a_afArg, int a_iArgc)
{ 
  if (!a_iArgc)	
    throw exception_type("too few arguments for function sum.");

  value_type fRes=0;
  for (int i=0; i<a_iArgc; ++i) fRes += a_afArg[i];
  return fRes;
}

//---------------------------------------------------------------------------
// mean value
value_type Parser::Avg(const value_type *a_afArg, int a_iArgc)
{ 
  if (!a_iArgc)	
    throw exception_type("too few arguments for function sum.");

  value_type fRes=0;
  for (int i=0; i<a_iArgc; ++i) fRes += a_afArg[i];
  return fRes/(double)a_iArgc;
}

//---------------------------------------------------------------------------
// minimum
value_type Parser::Min(const value_type *a_afArg, int a_iArgc)
{ 
    if (!a_iArgc)	
        throw exception_type("too few arguments for function min.");

    value_type fRes=a_afArg[0];
    for (int i=0; i<a_iArgc; ++i) fRes = std::min(fRes, a_afArg[i]);

    return fRes;
}

//---------------------------------------------------------------------------
// maximum
value_type Parser::Max(const value_type *a_afArg, int a_iArgc)
{ 
    if (!a_iArgc)	
        throw exception_type("too few arguments for function min.");

    value_type fRes=a_afArg[0];
    for (int i=0; i<a_iArgc; ++i) fRes = std::max(fRes, a_afArg[i]);

    return fRes;
}

//---------------------------------------------------------------------------
// Default value recognition callback
bool Parser::IsVal(const char_type *a_szExpr, int &a_iPos, value_type &a_fVal)
{
  stringstream_type stream(a_szExpr);
  value_type fVal(0);

  stream >> fVal;
  int iEnd = stream.tellg();    // Position after reading

  if (iEnd==-1)
    return false;

  a_iPos += iEnd;
  a_fVal = fVal;
  return true;
}

//---------------------------------------------------------------------------
/** \brief Constructor. 

  Call ParserBase class constructor and trigger Function, Operator and Constant initialization.
*/
Parser::Parser()
  :ParserBase()
  ,m_fEpsilon((value_type)1e-7)
{
  AddValIdent(IsVal);

  InitCharSets();
  InitFun();
  InitConst();
  InitOprt();
}

//---------------------------------------------------------------------------
/** Define the character sets. */
void Parser::InitCharSets()
{
  DefineNameChars("0123456789_abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ");
  DefineOprtChars("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ+-*^/?<>=#!$%&|~'_");
  DefineInfixOprtChars("/+-*^?<>=#!$%&|~'_");
}

//---------------------------------------------------------------------------
/** \brief Initialize the default functions. */
void Parser::InitFun()
{
  // trigonometric functions
  DefineFun("sin", Sin);
  DefineFun("cos", Cos);
  DefineFun("tan", Tan);
  // arcus functions
  DefineFun("asin", ASin);
  DefineFun("acos", ACos);
  DefineFun("atan", ATan);
  // hyperbolic functions
  DefineFun("sinh", Sinh);
  DefineFun("cosh", Cosh);
  DefineFun("tanh", Tanh);
  // arcus hyperbolic functions
  DefineFun("asinh", ASinh);
  DefineFun("acosh", ACosh);
  DefineFun("atanh", ATanh);
  // Logarithm functions
  DefineFun("log2", Log2);
  DefineFun("log10", Log10);
  DefineFun("log", Log10);
  DefineFun("ln", Ln);
  // misc
  DefineFun("exp", Exp);
  DefineFun("sqrt", Sqrt);
  DefineFun("sign", Sign);
  DefineFun("rint", Rint);
  DefineFun("abs", Abs);
  DefineFun("if", Ite);
  // Functions with variable number of arguments
  DefineFun("sum", Sum);
  DefineFun("avg", Avg);
  DefineFun("min", Min);
  DefineFun("max", Max);
}

//---------------------------------------------------------------------------
/** \brief Initialize operators. */
void Parser::InitConst()
{
  DefineConst("_pi", (value_type)PARSER_CONST_PI);
  DefineConst("_e", (value_type)PARSER_CONST_E);
}

//---------------------------------------------------------------------------
/** \brief Initialize operators. */
void Parser::InitOprt()
{
  DefineInfixOprt("-", UnaryMinus);
}

//---------------------------------------------------------------------------
/** \brief Numerically differentiate with regard to a variable. */
value_type Parser::Diff(value_type *a_Var, value_type a_fPos) const
{
  assert(m_fEpsilon);
  value_type fEpsilon( (a_fPos==0) ? (value_type)1e-10 : m_fEpsilon * a_fPos ),
             fRes(0), fBuf(*a_Var), f[4] = {0,0,0,0};

 *a_Var = a_fPos+2*fEpsilon;  f[0] = Eval();
 *a_Var = a_fPos+1*fEpsilon;  f[1] = Eval();
 *a_Var = a_fPos-1*fEpsilon;  f[2] = Eval();
 *a_Var = a_fPos-2*fEpsilon;  f[3] = Eval();
 *a_Var = fBuf; // restore variable

  fRes = (-f[0] + 8*f[1] - 8*f[2] + f[3]) / (12*fEpsilon);
  return fRes;
}

} // namespace mu