/*
    KmPlot - a math. function plotter for the KDE-Desktop

    SPDX-FileCopyrightText: 1998, 1999, 2000, 2002 Klaus-Dieter Möller <kd.moeller@t-online.de>
    SPDX-FileCopyrightText: 2006 David Saxton <david@bluehaze.org>

    This file is part of the KDE Project.
    KmPlot is part of the KDE-EDU Project.

    SPDX-License-Identifier: GPL-2.0-or-later

*/

// local includes
#include "parser.h"
#include "parseradaptor.h"
#include "settings.h"
#include "xparser.h"

// KDE includes
#include <KConfig>
#include <KLocalizedString>
#include <KMessageBox>

#include <QDebug>
#include <QList>

// standard c(++) includes
#include <assert.h>
#include <cmath>
#include <limits>
#include <locale.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>

double Parser::m_radiansPerAngleUnit = 0;

/**
 * List of predefined functions.
 * \note Some function names include other function names (e.g. "sinh" has the
 * string "sin" in it). The Parser will stop once it has found a matching
 * function name, so such functions must be in order of longest first.
 */
ScalarFunction Parser::scalarFunctions[ScalarCount] = {
    // Hyperbolic trig
    {"sinh", QString(), sinh}, // Sinus hyperbolicus
    {"cosh", QString(), cosh}, // Cosinus hyperbolicus
    {"tanh", QString(), tanh}, // Tangens hyperbolicus
    {"arcsinh", "arsinh", asinh}, // Area-sinus hyperbolicus = inverse of sinh
    {"arccosh", "arcosh", acosh}, // Area-cosinus hyperbolicus = inverse of cosh
    {"arctanh", "artanh", atanh}, // Area-tangens hyperbolicus = inverse of tanh

    // Reciprocal-hyperbolic
    {"cosech", QString(), cosech}, // Co-Secans hyperbolicus
    {"sech", QString(), sech}, // Secans hyperbolicus
    {"coth", QString(), coth}, // Co-Tangens hyperbolicus
    {"arccosech", "arcosech", arcosech}, // Area-co-secans hyperbolicus = inverse of cosech
    {"arcsech", "arsech", arsech}, // Area-secans hyperbolicus = inverse of sech
    {"arccoth", "arcoth", arcoth}, // Area-co-tangens hyperbolicus = inverse of coth

    // Reciprocal-trig
    {"cosec", QString(), lcosec}, // Co-Secans = 1/sin
    {"sec", QString(), lsec}, // Secans = 1/cos
    {"cot", QString(), lcot}, // Co-Tangens = 1/tan
    {"arccosec", "arcosech", larccosec}, // Arcus co-secans = inverse of cosec
    {"arcsec", "arsec", larcsec}, // Arcus secans = inverse of sec
    {"arccot", "arcot", larccot}, // Arcus co-tangens = inverse of cotan

    // Trigonometric functions
    {"sin", QString(), lsin}, // Sinus
    {"cos", QString(), lcos}, // Cosinus
    {"tan", QString(), ltan}, // Tangens
    {"arcsin", QString(), larcsin}, // Arcus sinus = inverse of sin
    {"arccos", QString(), larccos}, // Arcus cosinus = inverse of cos
    {"arctan", QString(), larctan}, // Arcus tangens = inverse of tan

    // Other
    {"sqrt", QString(), sqrt}, // Square root
    {"sqr", QString(), sqr}, // Square
    {"sign", QString(), sign}, // Signum
    {"H", QString(), heaviside}, // Heaviside step function
    {"log", QString(), log10}, // Logarithm base 10
    {"ln", QString(), log}, // Logarithm base e
    {"exp", QString(), exp}, // Exponential function base e
    {"abs", QString(), fabs}, // Absolute value
    {"floor", QString(), floor}, // round down to nearest integer
    {"ceil", QString(), ceil}, // round up to nearest integer
    {"round", QString(), round}, // round to nearest integer
    {"gamma", QString(), tgamma}, // gamma function
    {"lgamma", QString(), lgamma}, // log-gamma function
    {"factorial", QString(), factorial}, // factorial
    {"erfc", QString(), lerfc}, // error function
    {"erf", QString(), lerf}, // complementary error function

    // legendre
    {"P_0", QString(), legendre0}, // lengedre polynomial (n=0)
    {"P_1", QString(), legendre1}, // lengedre polynomial (n=1)
    {"P_2", QString(), legendre2}, // lengedre polynomial (n=2)
    {"P_3", QString(), legendre3}, // lengedre polynomial (n=3)
    {"P_4", QString(), legendre4}, // lengedre polynomial (n=4)
    {"P_5", QString(), legendre5}, // lengedre polynomial (n=5)
    {"P_6", QString(), legendre6}, // lengedre polynomial (n=6)
};

VectorFunction Parser::vectorFunctions[VectorCount] = {
    {"min", min}, // minimum of a set of reals
    {"max", max}, // maximum of a set of reals
    {"mod", mod}, // l2 modulus of a set of reals
};

/**
 * Order by longest string first, useful in parsing since we want to at each point
 * match the longest string first, so e.g. "sinh(x)" shouldn't be read as "sin(h) * x"
 */
class LengthOrderedString : public QString
{
public:
    LengthOrderedString()
    {
    }
    LengthOrderedString(const QString &s)
        : QString(s)
    {
    }

    bool operator<(const LengthOrderedString &other) const
    {
        return (length() > other.length()) || ((length() == other.length()) && (static_cast<const QString &>(*this) < static_cast<const QString &>(other)));
    }
};

// BEGIN class Parser
Parser::Parser()
    : m_sanitizer(this)
{
    m_evalPos = 0;
    m_nextFunctionID = 0;
    m_stack = new double[STACKSIZE];
    stkptr = m_stack;
    m_constants = new Constants;

    m_error = 0;
    m_ownEquation = 0;
    m_currentEquation = 0;
}

Parser::~Parser()
{
    for (Function *function : qAsConst(m_ufkt))
        delete function;
    delete m_ownEquation;
    delete m_constants;
    delete[] m_stack;
}

QStringList Parser::predefinedFunctions(bool includeAliases) const
{
    QStringList names;

    for (int func = 0; func < ScalarCount; ++func) {
        names << scalarFunctions[func].name1;
        if (includeAliases && !scalarFunctions[func].name2.isEmpty())
            names << scalarFunctions[func].name2;
    }

    for (int func = 0; func < VectorCount; ++func)
        names << vectorFunctions[func].name;

    return names;
}

QStringList Parser::userFunctions() const
{
    QStringList names;

    for (Function *f : qAsConst(m_ufkt)) {
        for (Equation *eq : qAsConst(f->eq)) {
            if (!eq->name().isEmpty())
                names << eq->name();
        }
    }

    names.sort();
    return names;
}

void Parser::reparseAllFunctions()
{
    for (Function *f : m_ufkt) {
        for (Equation *eq : f->eq)
            initEquation(eq);
    }
}

void Parser::setAngleMode(AngleMode mode)
{
    switch (mode) {
    case Radians:
        m_radiansPerAngleUnit = 1.0;
        break;

    case Degrees:
        m_radiansPerAngleUnit = M_PI / 180;
        break;
    }
}

uint Parser::getNewId()
{
    uint i = m_nextFunctionID;
    while (1) {
        if (!m_ufkt.contains(i)) {
            m_nextFunctionID = i + 1;
            return i;
        }
        ++i;
    }
}

double Parser::eval(const QString &str, Error *error, int *errorPosition)
{
    Error t1;
    if (!error)
        error = &t1;
    int t2;
    if (!errorPosition)
        errorPosition = &t2;

    if (!m_ownEquation)
        m_ownEquation = new Equation(Equation::Constant, 0);

    QString fName = XParser::self()->findFunctionName(QStringLiteral("f"), -1);

    QString eq = QStringLiteral("%1=%2").arg(fName).arg(str);
    if (!m_ownEquation->setFstr(eq, (int *)error, errorPosition)) {
        if (errorPosition)
            *errorPosition -= fName.length() + 1;
        return 0;
    }

    return fkt(m_ownEquation, Vector());
}

double Parser::fkt(uint id, int eq, double x)
{
    if (!m_ufkt.contains(id) || m_ufkt[id]->eq.size() <= eq) {
        *m_error = NoSuchFunction;
        return 0;
    }

    return fkt(m_ufkt[id]->eq[eq], x);
}

double Parser::fkt(Equation *eq, double x)
{
    Function *function = eq->parent();
    Q_ASSERT_X(function->type() != Function::Differential, "Parser::fkt", "Do not use this function directly! Instead, call XParser::differential");

    switch (function->type()) {
    case Function::Cartesian:
    case Function::Parametric:
    case Function::Polar: {
        Vector var(2);
        var[0] = x;
        var[1] = function->k;

        return fkt(eq, var);
    }

    case Function::Implicit: {
        Vector var(3);

        // Can only calculate when one of x, y is fixed
        assert(function->m_implicitMode != Function::UnfixedXY);

        if (function->m_implicitMode == Function::FixedX) {
            var[0] = function->x;
            var[1] = x;
        } else {
            // fixed y
            var[0] = x;
            var[1] = function->y;
        }
        var[2] = function->k;

        return fkt(eq, var);
    }

    case Function::Differential:
        return 0;
    }

    qWarning() << "Unknown function type!\n";
    return 0;
}

double Parser::fkt(Equation *eq, const Vector &x)
{
    if (eq->mem.isEmpty())
        return 0;

    // Consistency check: Make sure that we leave the stkptr at the same place
    // that we started it
    double *stkInitial = stkptr;

    double *pDouble;
    double (**pScalarFunction)(double);
    double (**pVectorFunction)(const Vector &);
    uint *pUint;
    eq->mptr = eq->mem.data();

    // Start with zero in our stackpointer
    //
    *stkptr = 0;

    while (1) {
        // 		qDebug() << "*eq->mptr: "<<int(*eq->mptr);

        switch (*eq->mptr++) {
        case KONST: {
            pDouble = (double *)eq->mptr;
            *stkptr = *pDouble++;
            eq->mptr = (char *)pDouble;
            break;
        }

        case VAR: {
            pUint = (uint *)eq->mptr;
            uint var = *pUint++;
            if (int(var) >= x.size()) {
                // Assume variable has value zero
                *stkptr = 0;
            } else
                *stkptr = x[var];
            eq->mptr = (char *)pUint;
            break;
        }

        case PUSH: {
            ++stkptr;
            break;
        }

        case PLUS: {
            stkptr[-1] += *stkptr;
            --stkptr;
            break;
        }

        case MINUS: {
            stkptr[-1] -= *stkptr;
            --stkptr;
            break;
        }

        case GT: {
            stkptr[-1] = (*(stkptr - 1) > *stkptr) ? 1 : 0;
            stkptr--;
            break;
        }

        case GE: {
            stkptr[-1] = (*(stkptr - 1) >= *stkptr) ? 1 : 0;
            stkptr--;
            break;
        }

        case LT: {
            stkptr[-1] = (*(stkptr - 1) < *stkptr) ? 1 : 0;
            stkptr--;
            break;
        }

        case LE: {
            stkptr[-1] = (*(stkptr - 1) <= *stkptr) ? 1 : 0;
            stkptr--;
            break;
        }

        case PM: {
            pUint = (uint *)eq->mptr;
            uint whichPM = *pUint++;
            eq->mptr = (char *)pUint;

            assert(int(whichPM) < eq->pmSignature().size());
            bool plus = eq->pmSignature()[whichPM];

            if (plus)
                stkptr[-1] += *stkptr;
            else
                stkptr[-1] -= *stkptr;

            --stkptr;
            break;
        }

        case MULT: {
            stkptr[-1] *= *stkptr;
            --stkptr;
            break;
        }

        case DIV: {
            if (*stkptr == 0.)
                *(--stkptr) = HUGE_VAL;
            else {
                stkptr[-1] /= *stkptr;
                --stkptr;
            }
            break;
        }

        case POW: {
            stkptr[-1] = pow(*(stkptr - 1), *stkptr);
            --stkptr;
            break;
        }

        case NEG: {
            *stkptr = -*stkptr;
            break;
        }

        case SQRT: {
            *stkptr = sqrt(*stkptr);
            break;
        }

        case FACT: {
            *stkptr = factorial(*stkptr);
            break;
        }

        case FKT_1: {
            pScalarFunction = (double (**)(double))eq->mptr;
            *stkptr = (*pScalarFunction++)(*stkptr);
            eq->mptr = (char *)pScalarFunction;
            break;
        }

        case FKT_N: {
            pUint = (uint *)eq->mptr;
            int numArgs = *pUint++;

            eq->mptr = (char *)pUint;

            pVectorFunction = (double (**)(const Vector &))eq->mptr;

            Vector args(numArgs);
            for (int i = 0; i < int(numArgs); ++i)
                args[i] = *(stkptr - numArgs + 1 + i);

            if (numArgs > 0)
                stkptr += 1 - numArgs;
            *stkptr = (*pVectorFunction++)(args);

            eq->mptr = (char *)pVectorFunction;
            break;
        }

        case UFKT: {
            pUint = (uint *)eq->mptr;
            uint id = *pUint++;
            uint id_eq = *pUint++;

            // The number of arguments being passed to the function
            int numArgs = *pUint++;

            Vector args(numArgs);
            for (int i = 0; i < numArgs; ++i)
                args[i] = *(stkptr - numArgs + 1 + i);

            if (m_ufkt.contains(id)) {
                if (numArgs > 0)
                    stkptr += 1 - numArgs;
                *stkptr = fkt(m_ufkt[id]->eq[id_eq], args);
            }

            eq->mptr = (char *)pUint;
            break;
        }

        case ENDE: {
            // If the stack isn't where we started at, then we've gone
            // up / down the wrong number of places - definitely a bug (and
            // will lead to crashes over time as memory rapidly runs out).
            assert(stkptr == stkInitial);
            return *stkptr;
        }
        case ERROR: {
            // something went wrong due to a incorrect formular or
            // missing const.
            qDebug() << "Error in equation " << eq->fstr();
            // Adjust stack again. Stack is wrong, only if we have a PUSH token
            // just before the ERROR token, afaik.
            while (stkptr != stkInitial) {
                stkptr--;
            }
            return *stkptr;
        }
        }
    }
}

int Parser::addFunction(const QString &str1, const QString &str2, Function::Type type, bool force)
{
    QString str[2] = {str1, str2};

    Function *temp = new Function(type);
    temp->setId(getNewId());

    for (int i = 0; i < 2; ++i) {
        if (str[i].isEmpty() || temp->eq.size() <= i)
            continue;

        int error;
        if (!temp->eq[i]->setFstr(str[i], &error, 0, force) && !force) {
            qDebug() << "could not set fstr to \"" << str[i] << "\"!  error:" << errorString(Error(error)) << "\n";
            delete temp;
            return -1;
        }

        bool duplicate = (fnameToID(temp->eq[i]->name()) != -1);
        if (temp->eq[i]->looksLikeFunction() && duplicate && !force) {
            qDebug() << "function name reused.\n";
            *m_error = FunctionNameReused;
            delete temp;
            return -1;
        }
    }

    m_ufkt[temp->id()] = temp;

    temp->plotAppearance(Function::Derivative0).color = XParser::self()->defaultColor(temp->id());
    // Better use QRandomGenerator::global()->generate() instead of qrand() since Qt 5.10
    temp->plotAppearance(Function::Derivative1).color = QColor::fromRgb(qrand());
    temp->plotAppearance(Function::Derivative2).color = QColor::fromRgb(qrand());
    temp->plotAppearance(Function::Integral).color = QColor::fromRgb(qrand());

    emit functionAdded(temp->id());
    return temp->id(); // return the unique ID-number for the function
}

void Parser::initEquation(Equation *eq, Error *error, int *errorPosition)
{
    Error t1;
    if (!error)
        error = &t1;
    int t2;
    if (!errorPosition)
        errorPosition = &t2;

    if (eq->parent())
        eq->parent()->clearFunctionDependencies();

    m_error = error;

    *m_error = ParseSuccess;
    *errorPosition = -1;

    m_currentEquation = eq;
    mem = &eq->mem;
    mptr = mem->data();
    m_pmAt = 0;

    m_eval = eq->fstr();
    m_sanitizer.fixExpression(&m_eval);
    m_evalRemaining = m_eval;
    m_evalPos = m_eval.indexOf('=') + 1;
    heir0();

    if (!evalRemaining().isEmpty() && *m_error == ParseSuccess)
        *m_error = SyntaxError;

    if (*m_error != ParseSuccess) {
        *errorPosition = m_sanitizer.realPos(m_evalPos);
        qDebug() << "add an error token for " << eq->fstr();
        // add an error token and let the user decide
        addToken(ERROR);
    }
    addToken(ENDE);
}

bool Parser::removeFunction(Function *item)
{
    // Build up a list of functions that need to be removed is this function is removed
    QList<Function *> toRemove;
    QStringList otherRemoveNames;
    QList<Function *> newFunctions; // Added since the last iteration

    toRemove << item;
    newFunctions << item;

    while (!newFunctions.isEmpty()) {
        const QList<Function *> currentFunctions = newFunctions;
        newFunctions.clear();

        for (Function *f : currentFunctions) {
            for (Function *other : qAsConst(m_ufkt)) {
                if ((other == f) || toRemove.contains(other))
                    continue;

                if (other->dependsOn(f)) {
                    toRemove << other;
                    otherRemoveNames << other->name();
                    newFunctions << other;
                }
            }
        }
    }

    if (toRemove.size() > 1) {
        KGuiItem buttonContinue = KStandardGuiItem::cont();
        buttonContinue.setText(i18n("Remove all"));

        int answer =
            KMessageBox::warningContinueCancel(0,
                                               i18n("The function %1 is depended upon by the following functions: %2. These must be removed in addition.",
                                                    item->name(),
                                                    otherRemoveNames.join(", ")),
                                               QString(),
                                               buttonContinue);

        if (answer == KMessageBox::Cancel)
            return false;
    }

    for (Function *f : qAsConst(toRemove)) {
        uint id = f->id();
        m_ufkt.remove(id);
        delete f;
        emit functionRemoved(id);
    }

    return true;
}

bool Parser::removeFunction(uint id)
{
    return m_ufkt.contains(id) && removeFunction(m_ufkt[id]);
}

void Parser::removeAllFunctions()
{
    while (!m_ufkt.isEmpty()) {
        Function *f = *m_ufkt.begin();
        int id = f->id();
        m_ufkt.remove(id);
        delete f;
        emit functionRemoved(id);
    }
}

uint Parser::countFunctions()
{
    return m_ufkt.count();
}

void Parser::heir0()
{
    heir1();

    if (*m_error != ParseSuccess)
        return;

    while (1) {
        if (m_eval.length() <= m_evalPos)
            return;

        QChar c = m_eval[m_evalPos];

        switch (c.unicode()) {
        default:
            return;

        case '<':
        case '>':
        case 0x2264: // less than or equal
        case 0x2265: // greater than or equal
            ++m_evalPos;
            addToken(PUSH);
            heir1();
            if (*m_error != ParseSuccess)
                return;
        }
        switch (c.unicode()) {
        case '<':
            addToken(LT);
            break;

        case '>':
            addToken(GT);
            break;

        case 0x2264: // less than or equal
            addToken(LE);
            break;

        case 0x2265: // greater than or equal
            addToken(GE);
            break;
        }
    }
}

void Parser::heir1()
{
    heir2();

    if (*m_error != ParseSuccess)
        return;

    while (1) {
        if (m_eval.length() <= m_evalPos)
            return;

        QChar c = m_eval[m_evalPos];

        switch (c.unicode()) {
        default:
            return;

        case 0xb1:
            if (m_pmAt >= MAX_PM) {
                *m_error = TooManyPM;
                return;
            }
            if (m_currentEquation == m_ownEquation) {
                *m_error = InvalidPM;
                return;
            }
            // no break
            Q_FALLTHROUGH();
        case '+':
        case '-':
            ++m_evalPos;
            addToken(PUSH);
            heir2();
            if (*m_error != ParseSuccess)
                return;
        }
        switch (c.unicode()) {
        case '+':
            addToken(PLUS);
            break;

        case '-':
            addToken(MINUS);
            break;

        case 0xb1:
            addToken(PM);
            adduint(m_pmAt++);
            break;
        }
    }
}

void Parser::heir2()
{
    if (match(SqrtSymbol)) // square root symbol
    {
        heir2();
        if (*m_error != ParseSuccess)
            return;
        addToken(SQRT);
    } else
        heir3();
}

void Parser::heir3()
{
    QChar c;
    heir4();
    if (*m_error != ParseSuccess)
        return;
    while (1) {
        if (m_eval.length() <= m_evalPos)
            return;

        c = m_eval[m_evalPos];
        switch (c.unicode()) {
        default:
            return;
        case '*':
        case '/':
            ++m_evalPos;
            addToken(PUSH);
            heir4();
            if (*m_error != ParseSuccess)
                return;
        }
        switch (c.unicode()) {
        case '*':
            addToken(MULT);
            break;
        case '/':
            addToken(DIV);
            break;
        }
    }
}

void Parser::heir4()
{
    if (match(QStringLiteral("-"))) {
        heir4();
        if (*m_error != ParseSuccess)
            return;
        addToken(NEG);
    } else if (match(QStringLiteral("+"))) {
        heir4();
    } else {
        heir5();
    }
}

void Parser::heir5()
{
    primary();
    if (*m_error != ParseSuccess)
        return;

    while (true) {
        if (match(QStringLiteral("^"))) {
            addToken(PUSH);
            heir4();
            if (*m_error != ParseSuccess)
                return;
            addToken(POW);
        } else if (match(QStringLiteral("!")))
            addToken(FACT);
        else
            return;
    }
}

void Parser::primary()
{
    // Notes:
    // - tryUserFunction has to go after tryVariable since differential
    //   equations treat the function name as a variable
    // - tryConstant has to go before tryUserFunction. This solves a problem,
    //   when a function and a constant share the same name

    tryFunction() || tryPredefinedFunction() || tryVariable() || tryConstant() || tryUserFunction() || tryNumber();
}

bool Parser::tryFunction()
{
    if (!match(QStringLiteral("(")) && !match(QStringLiteral(",")))
        return false;

    heir0();
    if (!match(QStringLiteral(")")) && !match(QStringLiteral(",")))
        *m_error = MissingBracket;
    return true;
}

bool Parser::tryPredefinedFunction()
{
    for (int i = 0; i < ScalarCount; ++i) {
        if (match(scalarFunctions[i].name1) || match(scalarFunctions[i].name2)) {
            primary();
            addToken(FKT_1);
            addfptr(scalarFunctions[i].mfadr);
            return true;
        }
    }
    for (int i = 0; i < VectorCount; ++i) {
        if (match(vectorFunctions[i].name)) {
            int argCount = readFunctionArguments();

            addToken(FKT_N);
            addfptr(vectorFunctions[i].mfadr, argCount);
            return true;
        }
    }

    return false;
}

bool Parser::tryVariable()
{
    const QStringList variables = m_currentEquation->variables();

    // Sort the parameters by size, so that when identifying parameters, want to
    // match e.g. "ab" before "a"
    typedef QMultiMap<int, QString> ISMap;
    ISMap sorted;
    for (const QString &var : variables)
        sorted.insert(-var.length(), var);

    for (const QString &var : qAsConst(sorted)) {
        if (match(var)) {
            addToken(VAR);
            adduint(variables.indexOf(var));
            return true;
        }
    }

    return false;
}

bool Parser::tryUserFunction()
{
    for (Function *it : qAsConst(m_ufkt)) {
        for (int i = 0; i < it->eq.size(); ++i) {
            if (!match(it->eq[i]->name()))
                continue;

            if (it->eq[i] == m_currentEquation || (m_currentEquation && it->dependsOn(m_currentEquation->parent()))) {
                *m_error = RecursiveFunctionCall;
                return true;
            }

            int argCount = readFunctionArguments();
            if (argCount != it->eq[i]->variables().size()) {
                *m_error = IncorrectArgumentCount;
                return true;
            }

            addToken(UFKT);
            addfptr(it->id(), i, argCount);
            if (m_currentEquation->parent())
                m_currentEquation->parent()->addFunctionDependency(it);

            return true;
        }
    }

    return false;
}

bool Parser::tryConstant()
{
#define CHECK_CONSTANT(a, b)                                                                                                                                   \
    if (match(a)) {                                                                                                                                            \
        addConstant(b);                                                                                                                                        \
        return true;                                                                                                                                           \
    }

    ConstantList constants = m_constants->list(Constant::All);

    QMap<LengthOrderedString, Constant> orderedConstants;
    for (ConstantList::iterator i = constants.begin(); i != constants.end(); ++i)
        orderedConstants[i.key()] = i.value();

    for (QMap<LengthOrderedString, Constant>::iterator i = orderedConstants.begin(); i != orderedConstants.end(); ++i)
        CHECK_CONSTANT(i.key(), i.value().value.value());

    // Or a predefined constant?
    CHECK_CONSTANT("pi", M_PI);
    CHECK_CONSTANT(PiSymbol, M_PI);
    CHECK_CONSTANT("e", M_E);
    CHECK_CONSTANT(InfinitySymbol, std::numeric_limits<double>::infinity());

    return false;
}

bool Parser::tryNumber()
{
    QByteArray remaining = evalRemaining().toLatin1();
    char *lptr = remaining.data();
    char *p = 0;
    // we converted all to "C" format in fixExpression
    char *oldLocale = setlocale(LC_NUMERIC, "C");
    double const w = strtod(lptr, &p);
    setlocale(LC_NUMERIC, oldLocale);
    if (lptr != p) {
        m_evalPos += p - lptr;
        addConstant(w);
        return true;
    }

    return false;
}

int Parser::readFunctionArguments()
{
    if (!evalRemaining().startsWith('('))
        return 0;

    int argCount = 0;
    bool argLeft = true;
    do {
        argCount++;
        primary();

        argLeft = m_eval.at(m_evalPos - 1) == ',';
        if (argLeft) {
            addToken(PUSH);
            m_evalPos--;
        }
    } while (*m_error == ParseSuccess && argLeft && !evalRemaining().isEmpty());

    return argCount;
}

void Parser::growEqMem(int growth)
{
    int pos = mptr - mem->data();
    mem->resize(mem->size() + growth);
    mptr = mem->data() + pos;
}

void Parser::addToken(Token token)
{
    growEqMem(sizeof(Token));
    *mptr++ = token;
}

void Parser::addConstant(double x)
{
    addToken(KONST);

    growEqMem(sizeof(double));
    double *pd = (double *)mptr;

    *pd++ = x;
    mptr = (char *)pd;
}

void Parser::adduint(uint x)
{
    growEqMem(sizeof(uint));
    uint *p = (uint *)mptr;
    *p++ = x;
    mptr = (char *)p;
}

void Parser::addfptr(double (*fadr)(double))
{
    typedef double (**sfPtr)(double);

    growEqMem(sizeof(sfPtr));
    // 	double (**pf)(double)=(double(**)(double))mptr;

    sfPtr pf = (sfPtr)mptr;
    *pf++ = fadr;
    mptr = (char *)pf;
}

void Parser::addfptr(double (*fadr)(const Vector &), int argCount)
{
    typedef double (**vfPtr)(const Vector &);

    growEqMem(sizeof(uint));
    uint *p = (uint *)mptr;
    *p++ = argCount;
    mptr = (char *)p;

    growEqMem(sizeof(vfPtr));
    vfPtr pf = (vfPtr)mptr;
    *pf++ = fadr;
    mptr = (char *)pf;
}

void Parser::addfptr(uint id, uint eq_id, uint args)
{
    growEqMem(3 * sizeof(uint));

    uint *p = (uint *)mptr;
    *p++ = id;
    *p++ = eq_id;
    *p++ = args;
    mptr = (char *)p;
}

int Parser::fnameToID(const QString &name)
{
    for (Function *it : qAsConst(m_ufkt)) {
        for (Equation *eq : qAsConst(it->eq)) {
            if (eq->looksLikeFunction() && (name == eq->name()))
                return it->id();
        }
    }
    return -1; // Name not found
}

// static
QString Parser::errorString(Error error)
{
    switch (error) {
    case ParseSuccess:
        return QString();

    case SyntaxError:
        return i18n("Syntax error");

    case MissingBracket:
        return i18n("Missing parenthesis");

    case StackOverflow:
        return i18n("Stack overflow");

    case FunctionNameReused:
        return i18n("Name of function is not free");

    case RecursiveFunctionCall:
        return i18n("recursive function not allowed");

    case EmptyFunction:
        return i18n("Empty function");

    case NoSuchFunction:
        return i18n("Function could not be found");

    case ZeroOrder:
        return i18n("The differential equation must be at least first-order");

    case TooManyPM:
        return i18n("Too many plus-minus symbols");

    case InvalidPM:
        return i18n("Invalid plus-minus symbol (expression must be constant)");

    case TooManyArguments:
        return i18n("The function has too many arguments");

    case IncorrectArgumentCount:
        return i18n("The function does not have the correct number of arguments");
    }

    return QString();
}

void Parser::displayErrorDialog(Error error)
{
    QString message(errorString(error));
    if (!message.isEmpty())
        KMessageBox::sorry(0, message, QStringLiteral("KmPlot"));
}

QString Parser::evalRemaining()
{
    /// note changing this code may need to change code in match() as well; similar
    int newLength = qMax(0, m_eval.length() - m_evalPos);
    if (newLength != m_evalRemaining.length())
        m_evalRemaining = m_eval.right(newLength);
    return m_evalRemaining;
}

bool Parser::match(const QString &lit)
{
    if (lit.isEmpty())
        return false;

    /// note changing this code may need to change code in evalRemaining() as well; similar
    // Do we need to update m_evalRemaining ?
    int newLength = qMax(0, m_eval.length() - m_evalPos);
    if (newLength != m_evalRemaining.length())
        evalRemaining();

    if (!m_evalRemaining.startsWith(lit))
        return false;

    m_evalPos += lit.length();
    return true;
}

Function *Parser::functionWithID(int id) const
{
    return m_ufkt.contains(id) ? m_ufkt[id] : 0;
}

// static
QString Parser::number(double value)
{
    QString str = QString::number(value, 'g', 16);
    str.replace('e', QLatin1String("*10^"));
    return str;
}
// END class Parser

// BEGIN predefined mathematical functions
double sqr(double x)
{
    return x * x;
}
double lsec(double x)
{
    return (1 / cos(x * Parser::radiansPerAngleUnit()));
}
double lcosec(double x)
{
    return (1 / sin(x * Parser::radiansPerAngleUnit()));
}
double lcot(double x)
{
    return (1 / tan(x * Parser::radiansPerAngleUnit()));
}
double larcsec(double x)
{
    return acos(1 / x) / Parser::radiansPerAngleUnit();
}
double larccosec(double x)
{
    return asin(1 / x) / Parser::radiansPerAngleUnit();
}
double larccot(double x)
{
    return (M_PI / 2 - atan(x)) / Parser::radiansPerAngleUnit();
}
double sech(double x)
{
    return (1 / cosh(x));
}
double cosech(double x)
{
    return (1 / sinh(x));
}
double coth(double x)
{
    return (1 / tanh(x));
}
double arsech(double x)
{
    return acosh(1 / x);
}
double arcosech(double x)
{
    return asinh(1 / x);
}
double arcoth(double x)
{
    return atanh(1 / x);
}
double lcos(double x)
{
    return cos(x * Parser::radiansPerAngleUnit());
}
double lsin(double x)
{
    return sin(x * Parser::radiansPerAngleUnit());
}
double ltan(double x)
{
    return tan(x * Parser::radiansPerAngleUnit());
}
double larccos(double x)
{
    return acos(x) / Parser::radiansPerAngleUnit();
}
double larcsin(double x)
{
    return asin(x) / Parser::radiansPerAngleUnit();
}
double larctan(double x)
{
    return atan(x) / Parser::radiansPerAngleUnit();
}
double factorial(double x)
{
    return tgamma(x + 1);
}
double legendre0(double)
{
    return 1.0;
}
double legendre1(double x)
{
    return x;
}
double legendre2(double x)
{
    return (3 * x * x - 1) / 2;
}
double legendre3(double x)
{
    return (5 * x * x * x - 3 * x) / 2;
}
double legendre4(double x)
{
    return (35 * x * x * x * x - 30 * x * x + 3) / 8;
}
double legendre5(double x)
{
    return (63 * x * x * x * x * x - 70 * x * x * x + 15 * x) / 8;
}
double legendre6(double x)
{
    return (231 * x * x * x * x * x * x - 315 * x * x * x * x + 105 * x * x - 5) / 16;
}

double sign(double x)
{
    if (x < 0.)
        return -1.;
    else if (x > 0.)
        return 1.;
    return 0.;
}

double heaviside(double x)
{
    if (x < 0.0)
        return 0.0;
    else if (x > 0.0)
        return 1.0;
    else
        return 0.5;
}

double min(const Vector &args)
{
    double best = HUGE_VAL;
    for (int i = 0; i < args.size(); ++i) {
        if (args[i] < best)
            best = args[i];
    }

    return best;
}

double max(const Vector &args)
{
    double best = -HUGE_VAL;
    for (int i = 0; i < args.size(); ++i) {
        if (args[i] > best)
            best = args[i];
    }

    return best;
}

double mod(const Vector &args)
{
    double squared = 0;
    for (int i = 0; i < args.size(); ++i)
        squared += args[i] * args[i];

    return std::sqrt(squared);
}

double lerf(double x)
{
    return erf(x);
}

double lerfc(double x)
{
    return erfc(x);
}

// END predefined mathematical functions

// BEGIN class ExpressionSanitizer
enum StringType { ConstantString, NumberString, UnknownLetter, FunctionString, Other };

ExpressionSanitizer::ExpressionSanitizer(Parser *parser)
    : m_parser(parser)
{
    m_str = 0l;
    m_decimalSymbol = QLocale().decimalPoint();
}

void ExpressionSanitizer::fixExpression(QString *str)
{
    m_str = str;

    m_map.resize(m_str->length());
    for (int i = 0; i < m_str->length(); ++i)
        m_map[i] = i;

    // greater-equal, less-equal with proper symbols
    // note that this must go before the next code for implicit equations, since
    // it removes the spurious equals signs
    replace(QStringLiteral(">="), GeSymbol);
    replace(QStringLiteral("<="), LeSymbol);

    // hack for implicit functions: change e.g. "y = x + 2" to "y - (x+2)" so
    // that they can be evaluated via equality with zero.
    if (str->count('=') > 1) {
        int equalsPos = str->lastIndexOf('=');
        replace(equalsPos, 1, QStringLiteral("-("));
        append(')');
    }

    stripWhiteSpace();

    // make sure all minus-like signs (including the actual unicode minus sign)
    // are represented by a dash (unicode 0x002d)
    QChar dashes[6] = {0x2012, 0x2013, 0x2014, 0x2015, 0x2053, 0x2212};
    for (unsigned i = 0; i < 6; ++i)
        replace(dashes[i], '-');

    // replace the proper unicode divide sign by the forward-slash
    replace(QChar(0xf7), '/');
    replace(QChar(0x2215), '/');

    // replace the unicode middle-dot for multiplication by the star symbol
    replace(QChar(0xd7), '*');
    replace(QChar(0x2219), '*');

    // minus-plus symbol to plus-minus symbol
    replace(QChar(0x2213), PmSymbol);

    // various power symbols
    replace(QChar(0x00B2), QStringLiteral("^2"));
    replace(QChar(0x00B3), QStringLiteral("^3"));
    replace(QChar(0x2070), QStringLiteral("^0"));
    replace(QChar(0x2074), QStringLiteral("^4"));
    replace(QChar(0x2075), QStringLiteral("^5"));
    replace(QChar(0x2076), QStringLiteral("^6"));
    replace(QChar(0x2077), QStringLiteral("^7"));
    replace(QChar(0x2078), QStringLiteral("^8"));
    replace(QChar(0x2079), QStringLiteral("^9"));

    // fractions
    replace(QChar(0x00BC), QStringLiteral("(1/4)"));
    replace(QChar(0x00BD), QStringLiteral("(1/2)"));
    replace(QChar(0x00BE), QStringLiteral("(3/4)"));
    replace(QChar(0x2153), QStringLiteral("(1/3)"));
    replace(QChar(0x2154), QStringLiteral("(2/3)"));
    replace(QChar(0x2155), QStringLiteral("(1/5)"));
    replace(QChar(0x2156), QStringLiteral("(2/5)"));
    replace(QChar(0x2157), QStringLiteral("(3/5)"));
    replace(QChar(0x2158), QStringLiteral("(4/5)"));
    replace(QChar(0x2159), QStringLiteral("(1/6)"));
    replace(QChar(0x215a), QStringLiteral("(5/6)"));
    replace(QChar(0x215b), QStringLiteral("(1/8)"));
    replace(QChar(0x215c), QStringLiteral("(3/8)"));
    replace(QChar(0x215d), QStringLiteral("(5/8)"));
    replace(QChar(0x215e), QStringLiteral("(7/8)"));

    // BEGIN replace e.g. |x+2| with abs(x+2)
    str->replace(AbsSymbol, '|');

    int maxDepth = str->count('(');
    QVector<bool> absAt(maxDepth + 1);
    for (int i = 0; i < maxDepth + 1; ++i)
        absAt[i] = false;

    int depth = 0;

    for (int i = 0; i < str->length(); ++i) {
        if (str->at(i) == '|') {
            if (absAt[depth]) {
                // Closing it
                replace(i, 1, QStringLiteral(")"));
                absAt[depth] = false;
            } else {
                // Opening it
                replace(i, 1, QStringLiteral("abs("));
                i += 3;
                absAt[depth] = true;
            }
        } else if (str->at(i) == '(')
            depth++;
        else if (str->at(i) == ')') {
            depth--;
            if (depth < 0)
                depth = 0;
        }
    }
    // END replace e.g. |x+2| with abs(x+2)

    if (m_decimalSymbol == QLatin1String(","))
        str->replace(QRegularExpression(QStringLiteral("(\\d),(\\d)")),
                     "\\1.\\2"); // if we use comma as a decimal separator it is reasonable to separate numbers in function arguments by comma with space
    else
        str->replace(m_decimalSymbol, QLatin1String(".")); // replace the locale decimal symbol with a '.' otherwise

    // BEGIN build up strings
    QMap<LengthOrderedString, StringType> strings;

    const QStringList predefinedFunctions = XParser::self()->predefinedFunctions(true);
    for (const QString &f : predefinedFunctions)
        strings[f] = FunctionString;

    for (Function *it : qAsConst(m_parser->m_ufkt)) {
        for (Equation *eq : qAsConst(it->eq))
            strings[eq->name()] = FunctionString;
    }

    const QStringList constantNames = m_parser->constants()->names();
    for (const QString &name : constantNames)
        strings[name] = ConstantString;
    strings[QStringLiteral("pi")] = ConstantString;
    // END build up strings

    strings.remove(QString());

    StringType prevType = Other;

    for (int i = 1; i < str->length();) {
        int incLength = 1;
        StringType currentType = Other;
        QChar ch = str->at(i);

        QString remaining = str->right(str->length() - i);

        QMap<LengthOrderedString, StringType>::const_iterator end = strings.constEnd();
        for (QMap<LengthOrderedString, StringType>::const_iterator it = strings.constBegin(); it != end; ++it) {
            if (!remaining.startsWith(it.key()))
                continue;

            currentType = it.value();
            incLength = it.key().length();
            break;
        }

        if (currentType == Other) {
            if (ch.isNumber() || (ch == '.'))
                currentType = NumberString;
        }

        if (currentType == Other) {
            if (ch.isLetter())
                currentType = UnknownLetter; // probably a variable
        }

        if (((currentType == FunctionString) || (ch == '(') || (currentType == UnknownLetter) || (currentType == ConstantString))
            && ((prevType == NumberString) || (prevType == ConstantString) || (prevType == UnknownLetter) || (str->at(i - 1) == ')'))) {
            insert(i, '*');
            incLength++;
        }

        prevType = currentType;
        i += incLength;
    }
}

void ExpressionSanitizer::stripWhiteSpace()
{
    int i = 0;

    while (i < m_str->length()) {
        if (m_str->at(i).isSpace()) {
            m_str->remove(i, 1);
            m_map.remove(i, 1);
        } else
            i++;
    }
}

void ExpressionSanitizer::remove(const QString &str)
{
    int at = 0;

    do {
        at = m_str->indexOf(str, at);
        if (at != -1) {
            m_map.remove(at, str.length());
            m_str->remove(at, str.length());
        }
    } while (at != -1);
}

void ExpressionSanitizer::remove(const QChar &str)
{
    remove(QString(str));
}

void ExpressionSanitizer::replace(QChar before, QChar after)
{
    m_str->replace(before, after);
}

void ExpressionSanitizer::replace(QChar before, const QString &after)
{
    if (after.isEmpty()) {
        remove(before);
        return;
    }

    int at = 0;

    do {
        at = m_str->indexOf(before, at);
        if (at != -1) {
            int to = m_map[at];
            for (int i = at + 1; i < at + after.length(); ++i)
                m_map.insert(i, to);

            m_str->replace(at, 1, after);
            at += after.length() - 1;
        }
    } while (at != -1);
}

void ExpressionSanitizer::replace(int pos, int len, const QString &after)
{
    int before = m_map[pos];
    m_map.remove(pos, len);
    m_map.insert(pos, after.length(), before);
    m_str->replace(pos, len, after);
}

void ExpressionSanitizer::replace(const QString &before, const QString &after)
{
    int index;
    while ((index = m_str->indexOf(before)) > -1)
        replace(index, before.length(), after);
}

void ExpressionSanitizer::insert(int i, QChar ch)
{
    m_map.insert(i, m_map[i]);
    m_str->insert(i, ch);
}

void ExpressionSanitizer::append(QChar str)
{
    m_map.insert(m_map.size(), m_map[m_map.size() - 1]);
    m_str->append(str);
}

int ExpressionSanitizer::realPos(int evalPos)
{
    if (m_map.isEmpty() || (evalPos < 0))
        return -1;

    if (evalPos >= m_map.size()) {
        // 		qWarning() << "evalPos="<<evalPos<<" is out of range.\n";
        // 		return m_map[ m_map.size() - 1 ];
        return -1;
    }

    return m_map[evalPos];
}

void ExpressionSanitizer::displayMap()
{
    QString out('\n');

    for (int i = 0; i < m_map.size(); ++i)
        out += QStringLiteral("%1").arg(m_map[i], 3);
    out += '\n';

    for (int i = 0; i < m_str->length(); ++i)
        out += "  " + (*m_str)[i];
    out += '\n';

    qDebug() << out;
}
// END class ExpressionSanitizer
