416 lines
14 KiB
C++
416 lines
14 KiB
C++
/***************************************************************************************************
|
|
**
|
|
** Copyright (C) 2013 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 "qmuparser.h"
|
|
|
|
#include <QtCore/qmath.h>
|
|
#include <math.h>
|
|
#include <QCoreApplication>
|
|
#include <QStaticStringData>
|
|
#include <QStringData>
|
|
#include <QStringDataPtr>
|
|
#include <QtGlobal>
|
|
#include <sstream>
|
|
#include <string>
|
|
|
|
#include "qmuparserdef.h"
|
|
#include "qmuparsererror.h"
|
|
|
|
using namespace std;
|
|
|
|
/**
|
|
* @file
|
|
* @brief Implementation of the standard floating point QmuParser.
|
|
*/
|
|
|
|
/**
|
|
* @brief Namespace for mathematical applications.
|
|
*/
|
|
namespace qmu
|
|
{
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
// Trigonometric function
|
|
qreal QmuParser::Sinh(qreal v)
|
|
{
|
|
return sinh(v);
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
qreal QmuParser::Cosh(qreal v)
|
|
{
|
|
return cosh(v);
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
qreal QmuParser::Tanh(qreal v)
|
|
{
|
|
return tanh(v);
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
qreal QmuParser::ASinh(qreal v)
|
|
{
|
|
return log(v + qSqrt(v * v + 1));
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
qreal QmuParser::ACosh(qreal v)
|
|
{
|
|
return log(v + qSqrt(v * v - 1));
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
qreal QmuParser::ATanh(qreal v)
|
|
{
|
|
return (0.5 * log((1 + v) / (1 - v)));
|
|
}
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
// Logarithm functions
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
// Logarithm base 2
|
|
qreal QmuParser::Log2(qreal v)
|
|
{
|
|
#ifdef MUP_MATH_EXCEPTIONS
|
|
if (v<=0)
|
|
{
|
|
throw QmuParserError(ecDOMAIN_ERROR, "Log2");
|
|
}
|
|
#endif
|
|
return log(v)/log(2.0);
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
// Logarithm base 10
|
|
qreal QmuParser::Log10(qreal v)
|
|
{
|
|
#ifdef MUP_MATH_EXCEPTIONS
|
|
if (v<=0)
|
|
{
|
|
throw QmuParserError(ecDOMAIN_ERROR, "Log10");
|
|
}
|
|
#endif
|
|
return log10(v);
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
// misc
|
|
qreal QmuParser::Abs(qreal v)
|
|
{
|
|
return qAbs(v);
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
qreal QmuParser::Rint(qreal v)
|
|
{
|
|
return qFloor(v + 0.5);
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
qreal QmuParser::Sign(qreal v)
|
|
{
|
|
return ((v<0) ? -1 : (v>0) ? 1 : 0);
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
qreal QmuParser::FMod(qreal number, qreal denom)
|
|
{
|
|
return fmod(number, denom);
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
/**
|
|
* @brief Callback for adding multiple values.
|
|
* @param [in] a_afArg Vector with the function arguments
|
|
* @param [in] a_iArgc The size of a_afArg
|
|
*/
|
|
qreal QmuParser::Sum(const qreal *a_afArg, int a_iArgc)
|
|
{
|
|
if (a_iArgc == 0)
|
|
{
|
|
throw QmuParserError(QCoreApplication::translate("QmuParser", "too few arguments for function sum.",
|
|
"parser error message"));
|
|
}
|
|
qreal fRes=0;
|
|
for (int i=0; i<a_iArgc; ++i)
|
|
{
|
|
fRes += a_afArg[i];
|
|
}
|
|
return fRes;
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
/**
|
|
* @brief Callback for averaging multiple values.
|
|
* @param [in] a_afArg Vector with the function arguments
|
|
* @param [in] a_iArgc The size of a_afArg
|
|
*/
|
|
qreal QmuParser::Avg(const qreal *a_afArg, int a_iArgc)
|
|
{
|
|
if (a_iArgc == 0)
|
|
{
|
|
throw QmuParserError(QCoreApplication::translate("QmuParser", "too few arguments for function sum.",
|
|
"parser error message"));
|
|
}
|
|
qreal fRes=0;
|
|
for (int i=0; i<a_iArgc; ++i)
|
|
{
|
|
fRes += a_afArg[i];
|
|
}
|
|
return fRes/static_cast<qreal>(a_iArgc);
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
/**
|
|
* @brief Callback for determining the minimum value out of a vector.
|
|
* @param [in] a_afArg Vector with the function arguments
|
|
* @param [in] a_iArgc The size of a_afArg
|
|
*/
|
|
qreal QmuParser::Min(const qreal *a_afArg, int a_iArgc)
|
|
{
|
|
if (a_iArgc == 0)
|
|
{
|
|
throw QmuParserError(QCoreApplication::translate("QmuParser", "too few arguments for function min.",
|
|
"parser error message"));
|
|
}
|
|
qreal fRes=a_afArg[0];
|
|
for (int i=0; i<a_iArgc; ++i)
|
|
{
|
|
fRes = qMin(fRes, a_afArg[i]);
|
|
}
|
|
return fRes;
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
/**
|
|
* @brief Callback for determining the maximum value out of a vector.
|
|
* @param [in] a_afArg Vector with the function arguments
|
|
* @param [in] a_iArgc The size of a_afArg
|
|
*/
|
|
qreal QmuParser::Max(const qreal *a_afArg, int a_iArgc)
|
|
{
|
|
if (a_iArgc == 0)
|
|
{
|
|
throw QmuParserError(QCoreApplication::translate("QmuParser", "too few arguments for function min.",
|
|
"parser error message"));
|
|
}
|
|
qreal fRes=a_afArg[0];
|
|
for (int i=0; i<a_iArgc; ++i)
|
|
{
|
|
fRes = qMax(fRes, a_afArg[i]);
|
|
}
|
|
return fRes;
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
/**
|
|
* @brief Default value recognition callback.
|
|
* @param [in] a_szExpr Pointer to the expression
|
|
* @param [in, out] a_iPos Pointer to an index storing the current position within the expression
|
|
* @param [out] a_fVal Pointer where the value should be stored in case one is found.
|
|
* @return 1 if a value was found 0 otherwise.
|
|
*/
|
|
int QmuParser::IsVal(const QString &a_szExpr, int *a_iPos, qreal *a_fVal, const std::locale &s_locale)
|
|
{
|
|
qreal fVal(0);
|
|
|
|
std::wstring a_szExprStd = a_szExpr.toStdWString();
|
|
stringstream_type stream(a_szExprStd);
|
|
stream.seekg(0); // todo: check if this really is necessary
|
|
stream.imbue(s_locale);
|
|
stream >> fVal;
|
|
stringstream_type::pos_type iEnd = stream.tellg(); // Position after reading
|
|
|
|
if (iEnd==static_cast<stringstream_type::pos_type>(-1))
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
*a_iPos += static_cast<int>(iEnd);
|
|
*a_fVal = fVal;
|
|
return 1;
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
/**
|
|
* @brief Constructor.
|
|
*
|
|
* Call QmuParserBase class constructor and trigger Function, Operator and Constant initialization.
|
|
*/
|
|
QmuParser::QmuParser():QmuParserBase()
|
|
{
|
|
AddValIdent(IsVal);
|
|
|
|
InitCharSets();
|
|
InitFun();
|
|
InitConst();
|
|
InitOprt();
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
/**
|
|
* @brief Define the character sets.
|
|
* @sa DefineNameChars, DefineOprtChars, DefineInfixOprtChars
|
|
*
|
|
* This function is used for initializing the default character sets that define
|
|
* the characters to be useable in function and variable names and operators.
|
|
*/
|
|
void QmuParser::InitCharSets()
|
|
{
|
|
DefineNameChars( QStringLiteral("0123456789_abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ") );
|
|
DefineOprtChars( QStringLiteral("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ+-*^/?<>=#!$%&|~'_{}") );
|
|
DefineInfixOprtChars( QStringLiteral("/+-*^?<>=#!$%&|~'_") );
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
/**
|
|
* @brief Initialize the default functions.
|
|
*/
|
|
void QmuParser::InitFun()
|
|
{
|
|
// trigonometric functions
|
|
DefineFun("sin", qSin);
|
|
DefineFun("cos", qCos);
|
|
DefineFun("tan", qTan);
|
|
// arcus functions
|
|
DefineFun("asin", qAsin);
|
|
DefineFun("acos", qAcos);
|
|
DefineFun("atan", qAtan);
|
|
DefineFun("atan2", qAtan2);
|
|
// 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", qLn);
|
|
// misc
|
|
DefineFun("exp", qExp);
|
|
DefineFun("sqrt", qSqrt);
|
|
DefineFun("sign", Sign);
|
|
DefineFun("rint", Rint);
|
|
DefineFun("abs", Abs);
|
|
DefineFun("fmod", FMod);
|
|
// Functions with variable number of arguments
|
|
DefineFun("sum", Sum);
|
|
DefineFun("avg", Avg);
|
|
DefineFun("min", Min);
|
|
DefineFun("max", Max);
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
/**
|
|
* @brief Initialize constants.
|
|
*
|
|
* By default the QmuParser recognizes two constants. Pi ("pi") and the eulerian
|
|
* number ("_e").
|
|
*/
|
|
void QmuParser::InitConst()
|
|
{
|
|
DefineConst("_pi", static_cast<qreal>(M_PI));
|
|
DefineConst("_e", static_cast<qreal>(M_E));
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
/**
|
|
* @brief Initialize operators.
|
|
*
|
|
* By default only the unary minus operator is added.
|
|
*/
|
|
void QmuParser::InitOprt()
|
|
{
|
|
DefineInfixOprt("-", UnaryMinus);
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
void QmuParser::OnDetectVar(const QString &pExpr, int &nStart, int &nEnd)
|
|
{
|
|
Q_UNUSED(pExpr);
|
|
Q_UNUSED(nStart);
|
|
Q_UNUSED(nEnd);
|
|
// this is just sample code to illustrate modifying variable names on the fly.
|
|
// I'm not sure anyone really needs such a feature...
|
|
/*
|
|
|
|
|
|
string sVar(pExpr->begin()+nStart, pExpr->begin()+nEnd);
|
|
string sRepl = std::string("_") + sVar + "_";
|
|
|
|
int nOrigVarEnd = nEnd;
|
|
cout << "variable detected!\n";
|
|
cout << " Expr: " << *pExpr << "\n";
|
|
cout << " Start: " << nStart << "\n";
|
|
cout << " End: " << nEnd << "\n";
|
|
cout << " Var: \"" << sVar << "\"\n";
|
|
cout << " Repl: \"" << sRepl << "\"\n";
|
|
nEnd = nStart + sRepl.length();
|
|
cout << " End: " << nEnd << "\n";
|
|
pExpr->replace(pExpr->begin()+nStart, pExpr->begin()+nOrigVarEnd, sRepl);
|
|
cout << " New expr: " << *pExpr << "\n";
|
|
*/
|
|
}
|
|
|
|
//---------------------------------------------------------------------------------------------------------------------
|
|
/**
|
|
* @brief Numerically differentiate with regard to a variable.
|
|
* @param [in] a_Var Pointer to the differentiation variable.
|
|
* @param [in] a_fPos Position at which the differentiation should take place.
|
|
* @param [in] a_fEpsilon Epsilon used for the numerical differentiation.
|
|
*
|
|
* Numerical differentiation uses a 5 point operator yielding a 4th order
|
|
* formula. The default value for epsilon is 0.00074 which is
|
|
* numeric_limits<double>::epsilon() ^ (1/5) as suggested in the muQmuParser
|
|
* forum:
|
|
*
|
|
* http://sourceforge.net/forum/forum.php?thread_id=1994611&forum_id=462843
|
|
*/
|
|
// cppcheck-suppress unusedFunction
|
|
qreal QmuParser::Diff(qreal *a_Var, qreal a_fPos, qreal a_fEpsilon) const
|
|
{
|
|
qreal fRes(0),
|
|
fBuf(*a_Var),
|
|
f[4] = {0, 0, 0, 0},
|
|
fEpsilon(a_fEpsilon);
|
|
|
|
// Backwards compatible calculation of epsilon inc case the user doesnt provide
|
|
// his own epsilon
|
|
if (qFuzzyIsNull(fEpsilon))
|
|
{
|
|
fEpsilon = qFuzzyIsNull(a_fPos) ? static_cast<qreal>(1e-10) : static_cast<qreal>(1e-7) * a_fPos;
|
|
}
|
|
|
|
*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 qmu
|