604 lines
20 KiB
C++
604 lines
20 KiB
C++
/***************************************************************************************************
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**
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** Copyright (C) 2013 Ingo Berg
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**
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** Permission is hereby granted, free of charge, to any person obtaining a copy of this
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** software and associated documentation files (the "Software"), to deal in the Software
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** without restriction, including without limitation the rights to use, copy, modify,
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** merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
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** permit persons to whom the Software is furnished to do so, subject to the following conditions:
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**
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** The above copyright notice and this permission notice shall be included in all copies or
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** substantial portions of the Software.
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**
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** THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT
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** NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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** NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
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** DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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** OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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**
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******************************************************************************************************/
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#include "qmuparser.h"
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#include <QCoreApplication>
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#include <QLineF>
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#include <QtGlobal>
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#include <sstream>
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#include <string>
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#include <QtDebug>
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#include <QtMath>
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#include "qmuparsererror.h"
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#include "../vmisc/defglobal.h"
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#include "qmudef.h"
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/**
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* @file
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* @brief Implementation of the standard floating point QmuParser.
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*/
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namespace
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{
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief CSR calcs special modeling case.
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* According to case we cut a piece with @p length, split up on distance @p split and rotate splited piece on
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* angle that will create arc with length @p arcLength.
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* @param length length of cut line
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* @param split distance between two pieces
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* @param arcLength length of arc that create two pieces after rotation
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* @return an angle the second piece should be rotated
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*/
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qreal CSR(qreal length, qreal split, qreal arcLength)
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{
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length = qAbs(length);
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arcLength = qAbs(arcLength);
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if (qFuzzyIsNull(length) || qFuzzyIsNull(split) || qFuzzyIsNull(arcLength))
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{
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return 0;
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}
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const qreal sign = std::copysign(1.0, split);
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const QLineF line(QPointF(0, 0), QPointF(0, length));
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QLineF tmp = line;
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tmp.setAngle(tmp.angle()+90.0*sign);
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tmp.setLength(split);
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QPointF p1 = tmp.p2();
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tmp = QLineF(QPointF(0, length), QPointF(0, 0));
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tmp.setAngle(tmp.angle()-90.0*sign);
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tmp.setLength(split);
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QPointF p2 = tmp.p2();
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const QLineF line2(p1, p2);
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qreal angle = 180;
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qreal arcL = INT_MAX;
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do
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{
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if (arcL > arcLength)
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{
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angle = angle - angle/2.0;
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}
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else if (arcL < arcLength)
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{
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angle = angle + angle/2.0;
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}
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else
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{
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return angle;
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}
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if (angle < 0.00001 || angle >= 360)
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{
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return 0;
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}
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tmp = line2;
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tmp.setAngle(tmp.angle()+angle*sign);
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QPointF crosPoint;
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#if QT_VERSION >= QT_VERSION_CHECK(5, 14, 0)
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const auto type = line.intersects(tmp, &crosPoint);
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#else
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const auto type = line.intersect(tmp, &crosPoint);
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#endif
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if (type == QLineF::NoIntersection)
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{
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return 0;
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}
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QLineF radius(crosPoint, tmp.p2());
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const qreal arcAngle = sign > 0 ? line.angleTo(radius): radius.angleTo(line);
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arcL = (M_PI*radius.length())/180.0 * arcAngle;
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}
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while(qAbs(arcL - arcLength) > (0.5/*mm*/ / 25.4) * PrintDPI);
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return angle;
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}
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}
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/**
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* @brief Namespace for mathematical applications.
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*/
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namespace qmu
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{
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//---------------------------------------------------------------------------------------------------------------------
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// Trigonometric function
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qreal QmuParser::DegreeToRadian(qreal deg)
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{
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return qDegreesToRadians(deg);
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::RadianToDegree(qreal rad)
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{
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return qRadiansToDegrees(rad);
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::Sinh(qreal v)
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{
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return sinh(v);
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::ASinh(qreal v)
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{
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return log(v + qSqrt(v * v + 1));
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::Cosh(qreal v)
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{
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return cosh(v);
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::ACosh(qreal v)
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{
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return log(v + qSqrt(v * v - 1));
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::Tanh(qreal v)
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{
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return tanh(v);
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::ATanh(qreal v)
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{
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return (0.5 * log((1 + v) / (1 - v)));
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::SinD(qreal v)
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{
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return qSin(qDegreesToRadians(v));
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::ASinD(qreal v)
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{
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return qRadiansToDegrees(qAsin(v));
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::CosD(qreal v)
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{
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return qCos(qDegreesToRadians(v));
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::ACosD(qreal v)
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{
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return qRadiansToDegrees(qAcos(v));
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::TanD(qreal v)
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{
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return qTan(qDegreesToRadians(v));
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::ATanD(qreal v)
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{
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return qRadiansToDegrees(qAtan(v));
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}
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//---------------------------------------------------------------------------------------------------------------------
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// Logarithm functions
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//---------------------------------------------------------------------------------------------------------------------
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// Logarithm base 2
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qreal QmuParser::Log2(qreal v)
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{
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#ifdef MUP_MATH_EXCEPTIONS
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if (v<=0)
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{
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throw QmuParserError(ecDOMAIN_ERROR, "Log2");
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}
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#endif
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return log(v)/log(2.0);
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}
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//---------------------------------------------------------------------------------------------------------------------
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// Logarithm base 10
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qreal QmuParser::Log10(qreal v)
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{
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#ifdef MUP_MATH_EXCEPTIONS
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if (v<=0)
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{
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throw QmuParserError(ecDOMAIN_ERROR, "Log10");
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}
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#endif
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return log10(v);
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}
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//---------------------------------------------------------------------------------------------------------------------
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// misc
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qreal QmuParser::Abs(qreal v)
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{
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return qAbs(v);
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::Rint(qreal v)
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{
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return qFloor(v + 0.5);
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::R2CM(qreal v)
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{
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return Rint(v*10.0)/10.0;
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::CSRCm(qreal length, qreal split, qreal arcLength)
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{
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length = ((length * 10.0) / 25.4) * PrintDPI;
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split = ((split * 10.0) / 25.4) * PrintDPI;
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arcLength = ((arcLength * 10.0) / 25.4) * PrintDPI;
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return CSR(length, split, arcLength);
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::CSRInch(qreal length, qreal split, qreal arcLength)
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{
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length = length * PrintDPI;
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split = split * PrintDPI;
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arcLength = arcLength * PrintDPI;
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return CSR(length, split, arcLength);
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::Sign(qreal v)
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{
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return ((v<0) ? -1 : (v>0) ? 1 : 0);
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal QmuParser::FMod(qreal number, qreal denom)
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{
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return fmod(number, denom);
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief Callback for adding multiple values.
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* @param [in] a_afArg Vector with the function arguments
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* @param [in] a_iArgc The size of a_afArg
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*/
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qreal QmuParser::Sum(const qreal *a_afArg, qmusizetype a_iArgc)
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{
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if (a_iArgc == 0)
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{
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throw QmuParserError(QCoreApplication::translate("QmuParser", "too few arguments for function sum.",
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"parser error message"));
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}
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qreal fRes=0;
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for (int i=0; i<a_iArgc; ++i)
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{
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fRes += a_afArg[i];
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}
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return fRes;
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief Callback for averaging multiple values.
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* @param [in] a_afArg Vector with the function arguments
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* @param [in] a_iArgc The size of a_afArg
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*/
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qreal QmuParser::Avg(const qreal *a_afArg, qmusizetype a_iArgc)
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{
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if (a_iArgc == 0)
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{
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throw QmuParserError(QCoreApplication::translate("QmuParser", "too few arguments for function sum.",
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"parser error message"));
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}
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qreal fRes=0;
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for (int i=0; i<a_iArgc; ++i)
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{
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fRes += a_afArg[i];
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}
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return fRes/static_cast<qreal>(a_iArgc);
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief Callback for determining the minimum value out of a vector.
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* @param [in] a_afArg Vector with the function arguments
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* @param [in] a_iArgc The size of a_afArg
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*/
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qreal QmuParser::Min(const qreal *a_afArg, qmusizetype a_iArgc)
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{
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if (a_iArgc == 0)
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{
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throw QmuParserError(QCoreApplication::translate("QmuParser", "too few arguments for function min.",
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"parser error message"));
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}
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qreal fRes=a_afArg[0];
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for (int i=0; i<a_iArgc; ++i)
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{
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fRes = qMin(fRes, a_afArg[i]);
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}
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return fRes;
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief Callback for determining the maximum value out of a vector.
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* @param [in] a_afArg Vector with the function arguments
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* @param [in] a_iArgc The size of a_afArg
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*/
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qreal QmuParser::Max(const qreal *a_afArg, qmusizetype a_iArgc)
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{
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if (a_iArgc == 0)
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{
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throw QmuParserError(QCoreApplication::translate("QmuParser", "too few arguments for function min.",
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"parser error message"));
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}
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qreal fRes=a_afArg[0];
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for (int i=0; i<a_iArgc; ++i)
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{
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fRes = qMax(fRes, a_afArg[i]);
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}
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return fRes;
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief Default value recognition callback.
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* @param [in] a_szExpr Pointer to the expression
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* @param [in, out] a_iPos Pointer to an index storing the current position within the expression
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* @param [out] a_fVal Pointer where the value should be stored in case one is found.
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* @return 1 if a value was found 0 otherwise.
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*/
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int QmuParser::IsVal(const QString &a_szExpr, qmusizetype *a_iPos, qreal *a_fVal, const QLocale &locale, bool cNumbers,
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const QChar &decimal, const QChar &thousand)
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{
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qreal fVal(0);
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qmusizetype pos = ReadVal(a_szExpr, fVal, locale != QLocale::c() && cNumbers ? QLocale::c() : locale, decimal,
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thousand);
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if (pos == -1)
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{
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return 0;
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}
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*a_iPos += pos;
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*a_fVal = fVal;
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return 1;
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief Constructor.
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*
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* Call QmuParserBase class constructor and trigger Function, Operator and Constant initialization.
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*/
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QmuParser::QmuParser():QmuParserBase()
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{
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AddValIdent(IsVal);
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Init();
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief Define the character sets.
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* @sa DefineNameChars, DefineOprtChars, DefineInfixOprtChars
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*
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* This function is used for initializing the default character sets that define
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* the characters to be useable in function and variable names and operators.
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*/
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void QmuParser::InitCharSets()
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{
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DefineNameChars( QStringLiteral("0123456789_abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ") );
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DefineOprtChars( QStringLiteral("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ+-*^/?<>=#!$%&|~'_{}") );
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DefineInfixOprtChars( QStringLiteral("/+-*^?<>=#!$%&|~'_") );
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief Initialize the default functions.
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*/
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void QmuParser::InitFun()
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{
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// trigonometric helper functions
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DefineFun(QStringLiteral("degTorad"), DegreeToRadian);
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DefineFun(QStringLiteral("radTodeg"), RadianToDegree);
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#if QT_VERSION >= QT_VERSION_CHECK(6, 0, 0)
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#define QSIN_FUN qSin<qreal>
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#define QCOS_FUN qCos<qreal>
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#define QTAN_FUN qTan<qreal>
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#define QASIN_FUN qAsin<qreal>
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#define QACOS_FUN qAcos<qreal>
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#define QATAN_FUN qAtan<qreal>
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#define QATAN2_FUN qAtan2<qreal, qreal>
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#define QLN_FUN qLn<qreal>
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#define QEXP_FUN qExp<qreal>
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#define QSQRT_FUN qSqrt<qreal>
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#else
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#define QSIN_FUN qSin
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#define QCOS_FUN qCos
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#define QTAN_FUN qTan
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#define QASIN_FUN qAsin
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#define QACOS_FUN qAcos
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#define QATAN_FUN qAtan
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#define QATAN2_FUN qAtan2
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#define QLN_FUN qLn
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#define QEXP_FUN qExp
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#define QSQRT_FUN qSqrt
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#endif
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// trigonometric functions
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DefineFun(QStringLiteral("sin"), QSIN_FUN);
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DefineFun(QStringLiteral("cos"), QCOS_FUN);
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DefineFun(QStringLiteral("tan"), QTAN_FUN);
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DefineFun(QStringLiteral("sinD"), SinD);
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DefineFun(QStringLiteral("cosD"), CosD);
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DefineFun(QStringLiteral("tanD"), TanD);
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// arcus functions
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DefineFun(QStringLiteral("asin"), QASIN_FUN);
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DefineFun(QStringLiteral("acos"), QACOS_FUN);
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DefineFun(QStringLiteral("atan"), QATAN_FUN);
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DefineFun(QStringLiteral("atan2"), QATAN2_FUN);
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DefineFun(QStringLiteral("asinD"), ASinD);
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DefineFun(QStringLiteral("acosD"), ACosD);
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DefineFun(QStringLiteral("atanD"), ATanD);
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// hyperbolic functions
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DefineFun(QStringLiteral("sinh"), Sinh);
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DefineFun(QStringLiteral("cosh"), Cosh);
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DefineFun(QStringLiteral("tanh"), Tanh);
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// arcus hyperbolic functions
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DefineFun(QStringLiteral("asinh"), ASinh);
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DefineFun(QStringLiteral("acosh"), ACosh);
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DefineFun(QStringLiteral("atanh"), ATanh);
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// Logarithm functions
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DefineFun(QStringLiteral("log2"), Log2);
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DefineFun(QStringLiteral("log10"), Log10);
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DefineFun(QStringLiteral("log"), Log10);
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DefineFun(QStringLiteral("ln"), QLN_FUN);
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// misc
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DefineFun(QStringLiteral("exp"), QEXP_FUN);
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DefineFun(QStringLiteral("sqrt"), QSQRT_FUN);
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DefineFun(QStringLiteral("sign"), Sign);
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DefineFun(QStringLiteral("rint"), Rint);
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DefineFun(QStringLiteral("r2cm"), R2CM);
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DefineFun(QStringLiteral("csrCm"), CSRCm);
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DefineFun(QStringLiteral("csrInch"), CSRInch);
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DefineFun(QStringLiteral("abs"), Abs);
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DefineFun(QStringLiteral("fmod"), FMod);
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// Functions with variable number of arguments
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DefineFun(QStringLiteral("sum"), Sum);
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DefineFun(QStringLiteral("avg"), Avg);
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DefineFun(QStringLiteral("min"), Min);
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DefineFun(QStringLiteral("max"), Max);
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief Initialize constants.
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*
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* By default the QmuParser recognizes two constants. Pi ("pi") and the eulerian
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* number ("_e").
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*/
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void QmuParser::InitConst()
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{
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DefineConst(QStringLiteral("_pi"), static_cast<qreal>(M_PI));
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DefineConst(QStringLiteral("_e"), static_cast<qreal>(M_E));
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief Initialize operators.
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*
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* By default only the unary minus operator is added.
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*/
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void QmuParser::InitOprt()
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{
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DefineInfixOprt(LocaleNegativeSign(m_locale), UnaryMinus);
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}
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//---------------------------------------------------------------------------------------------------------------------
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void QmuParser::OnDetectVar(const QString &pExpr, qmusizetype &nStart, qmusizetype &nEnd)
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{
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Q_UNUSED(pExpr)
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Q_UNUSED(nStart)
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Q_UNUSED(nEnd)
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// this is just sample code to illustrate modifying variable names on the fly.
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// I'm not sure anyone really needs such a feature...
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/*
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string sVar(pExpr->begin()+nStart, pExpr->begin()+nEnd);
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string sRepl = std::string("_") + sVar + "_";
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int nOrigVarEnd = nEnd;
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cout << "variable detected!\n";
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cout << " Expr: " << *pExpr << "\n";
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cout << " Start: " << nStart << "\n";
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cout << " End: " << nEnd << "\n";
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cout << " Var: \"" << sVar << "\"\n";
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cout << " Repl: \"" << sRepl << "\"\n";
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nEnd = nStart + sRepl.length();
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cout << " End: " << nEnd << "\n";
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pExpr->replace(pExpr->begin()+nStart, pExpr->begin()+nOrigVarEnd, sRepl);
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cout << " New expr: " << *pExpr << "\n";
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*/
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief Numerically differentiate with regard to a variable.
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* @param [in] a_Var Pointer to the differentiation variable.
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* @param [in] a_fPos Position at which the differentiation should take place.
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* @param [in] a_fEpsilon Epsilon used for the numerical differentiation.
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|
*
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* Numerical differentiation uses a 5 point operator yielding a 4th order
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|
* formula. The default value for epsilon is 0.00074 which is
|
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* numeric_limits<double>::epsilon() ^ (1/5) as suggested in the muQmuParser
|
|
* forum:
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*
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|
* http://sourceforge.net/forum/forum.php?thread_id=1994611&forum_id=462843
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*/
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// cppcheck-suppress unusedFunction
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qreal QmuParser::Diff(qreal *a_Var, qreal a_fPos, qreal a_fEpsilon) const
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|
{
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|
qreal fRes(0),
|
|
fBuf(*a_Var),
|
|
f[4] = {0, 0, 0, 0},
|
|
fEpsilon(a_fEpsilon);
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|
|
|
// 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;
|
|
}
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|
|
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*a_Var = a_fPos+2 * fEpsilon; f[0] = Eval();
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|
*a_Var = a_fPos+1 * fEpsilon; f[1] = Eval();
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|
*a_Var = a_fPos-1 * fEpsilon; f[2] = Eval();
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|
*a_Var = a_fPos-2 * fEpsilon; f[3] = Eval();
|
|
*a_Var = fBuf; // restore variable
|
|
|
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fRes = (-f[0] + 8*f[1] - 8*f[2] + f[3]) / (12*fEpsilon);
|
|
return fRes;
|
|
}
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|
} // namespace qmu
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