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Thread: Parser for mathematic expression from QString

  1. 7th May 2018, 15:39 #1
    sr1s
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    Default Parser for mathematic expression from QString

    Hello!
    I try to use a parser for simple math expressions from a QString, as 3+2.(5^2)/9....and so on (no variables to calculate, just numbers). I started with a recursive-descent parser, but then I found a simpler solution with QJSEngine:
    Qt Code: 
    1. #include "math.h"
    2. #include "expression_calc.h"
    3. #include "ui_expression_calc.h"
    4. #include "QDebug"
    5. #include <QApplication>
    6. #include <QJSEngine>
    7. #include <QJSValue>
    8. #include <QObject>
    9.  
    10.  
    11. Expression_calc::Expression_calc(QWidget *parent) :
    12.     QMainWindow(parent),
    13.     ui(new Ui::Expression_calc)
    14. {
    15.     ui->setupUi(this);
    16.  
    17.    }
    18.  
    19. Expression_calc::~Expression_calc()
    20. {
    21.    delete ui;
    22. }
    23.  
    24. void Expression_calc::on_CalcButton_clicked()
    25. {
    26.     QString expression= ui->exp->text();
    27.     QJSEngine parsexpression;
    28.     double result=parsexpression.evaluate(expression).toNumber();
    29.     ui->Result->setText(QString::number(result));
    30. }
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    Ok, very simply, ...but this method can interpret just +,-,*,/,()...
    I decide to manipulate the main QString expression with a
    Qt Code: 
    1. expression.replace("sqrt","Math.sqrt");
    2. expression.replace("abs","Math.abs");
    3. expression.replace("cos","Math.cos");
    4. ......
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    Not very elegant, but a fast solution. In add, as I have to store the expressions, I can save the corrected versions.
    All it works, except for the damned "^". Math requires "pow(3,2)" instead of common expression 3^2, does someone have a fast solution to workaround this, or you suggest to return to a recursive-descent parser?
    Thanks!
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  2. 7th May 2018, 17:37 #2
    d_stranz's Avatar
    d_stranz
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    Default Re: Parser for mathematic expression from QString

    Write yourself a QRegularExpression string match that pre-processes your input string, looking for "expr1^expr2" and substitutes "pow( expr1, expr2)" in the same way as you replace your other expressions.

    Does the JS parser recognize "**" for exponentiation? That could be an even simpler search and replace.
    <=== The Great Pumpkin says ===>
    Please use CODE tags when posting source code so it is more readable. Click "Go Advanced" and then the "#" icon to insert the tags. Paste your code between them.
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  3. 7th May 2018, 19:55 #3
    sr1s
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    Default Re: Parser for mathematic expression from QString

    I tried with "**" , hoping to have the same behavior as Java... but it didn't work. But your suggestion seems to be the right way, I'll try it.
    Thank you very much!
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  4. 8th May 2018, 10:44 #4
    sr1s
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    Default Re: Parser for mathematic expression from QString

    I followed your suggestion, and I solved my problems!
    Perhaps, with more knowledge, I could do better, but for now it's ok. The main problem is that RegularExpression considers "+" as a part of a number, and also the hierarchy of function didn't work well, so I "frozen" the operators (changing them with PLUS, MINUS, etc.), unfreezing them when I need... By now it goes correctly for the main functions, I have to implement the trigonometric and ABS ones, (now, as program simplifies expression between brackets, "ABS(-5)" becomes "ABS-5" ->nan), but it shouldn't be a great problem.

    I found a useful help using https://regex101.com/, it's simpler to understand QRegularEspression's syntax than compiling the code each time

    This is the code:
    Qt Code: 
    1. #include "math.h"
    2. #include "expression_calc.h"
    3. #include "ui_expression_calc.h"
    4. #include "QDebug"
    5. #include <QApplication>
    6. #include <QJSEngine>
    7. #include <QJSValue>
    8. #include <QObject>
    9.  
    10. Expression_calc::Expression_calc(QWidget *parent) :
    11.     QMainWindow(parent),
    12.     ui(new Ui::Expression_calc)
    13. {
    14.     ui->setupUi(this);
    15.  
    16.    }
    17.  
    18. Expression_calc::~Expression_calc()
    19. {
    20.    delete ui;
    21. }
    22.  
    23. void Expression_calc::on_CalcButton_clicked()
    24. {
    25.     QString expression= ui->exp->text();
    26.     QString exp1,exp2;
    27.     expression.replace("sin","Math.sin");
    28.     expression.replace("cos","Math.cos");
    29.     expression.replace("tan","Math.tan");
    30.      //.... and so on for trigonometrical functions)
    31.  
    32.     expression.replace("sqrt","Math.sqrt");
    33.     expression.replace("(","[");
    34.     expression.replace(")","]");
    35.     expression.replace("^","POW");
    36.     expression.replace("+","PLUS");
    37.     expression.replace("-","MINUS");
    38.     expression.replace("*","MULT");
    39.     expression.replace("/","DIV");
    40.  
    41.      while (expression.contains("[")) //START SOLVING EXPRESSIONS BETWEEN BRACKETS
    42.      {
    43.  
    44.          QRegularExpression rep("\\[([^\\]]+)\\]");
    45.            QRegularExpressionMatch matchp = rep.match(expression);
    46.            QString expp_w_brackets = matchp.captured(0); //original expression with brakets
    47.            QString expp = matchp.captured(1);//expression without brakets
    48.            expp.replace ("PLUS","+");
    49.            expp.replace ("MINUS","-");
    50.            expp.replace("MULT","*");
    51.            expp.replace("DIV","/");
    52.  
    53.            QJSEngine parsexpressionp;
    54.            double resultp=parsexpressionp.evaluate(expp).toNumber();
    55.            QString BraketResult=(QString::number(resultp));
    56.            expression.replace(""+expp_w_brackets+"" ,""+BraketResult+"");
    57. }
    58.  
    59.     while (expression.contains("POW")) //SOLVE POE EXPRESSION
    60.     {
    61.         QRegularExpression re1("(\\d+.\\d+POW)|(\\d+POW)");
    62.         QRegularExpressionMatch match1 = re1.match(expression);
    63.  
    64.         QRegularExpression re2("(POW\\d+.\\d+)|(POW\\d+)");
    65.         QRegularExpressionMatch match2 = re2.match(expression);
    66.  
    67.  
    68.         if (match1.hasMatch())
    69.         {
    70.             exp1 = match1.captured(0);
    71.             exp1.replace("POW","");
    72.         }
    73.  
    74.         if (match2.hasMatch())
    75.         {
    76.             exp2 = match2.captured(0);
    77.             exp2.replace("POW","");
    78.               }
    79.  
    80.  
    81.         expression.replace (""+exp1+"" "POW"""+exp2+"" , "Math.pow(" ""+exp1+"" ","  ""+exp2+""  ")");
    82.  
    83.      }
    84.     expression.replace("[","(");
    85.     expression.replace("]",")");
    86.     expression.replace ("PLUS","+");
    87.     expression.replace ("MINUS","-");
    88.     expression.replace("MULT","*");
    89.     expression.replace("DIV","/");
    90.     QJSEngine parsexpression;
    91.     double result=parsexpression.evaluate(expression).toNumber();
    92.     ui->Result->setText(QString::number(result));
    93. }
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    Last edited by sr1s; 8th May 2018 at 11:30.
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  5. 8th May 2018, 15:58 #5
    sr1s
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    Default Re: Parser for mathematic expression from QString

    I have to correct a mistake (if I had "2^(6/3)", the code returns a nan), in a second time I'll create a pow() function to have a more clear code...
    For the problem abs(-1)->abs1, or cos(0) -> cos0, a very rough solution: I change, for example, abs(-1) into math.abs{-1), and then, before processing expression, replace again "{" with "(".. Very ugly, but it's enough to avoid the transforming into math.abs-1...
    So, the code is this:
    Qt Code: 
    1. #include "math.h"
    2. #include "expression_calc.h"
    3. #include "ui_expression_calc.h"
    4. #include "QDebug"
    5. #include <QApplication>
    6. #include <QJSEngine>
    7. #include <QJSValue>
    8. #include <QObject>
    9.  
    10. Expression_calc::Expression_calc(QWidget *parent) :
    11.     QMainWindow(parent),
    12.     ui(new Ui::Expression_calc)
    13. {
    14.     ui->setupUi(this);
    15.  
    16.    }
    17.  
    18. Expression_calc::~Expression_calc()
    19. {
    20.    delete ui;
    21. }
    22.  
    23. void Expression_calc::on_CalcButton_clicked()
    24. {
    25.     QString expression= ui->exp->text();
    26.     QString exp1,exp2;
    27.  
    28.     expression.replace("pi","Math.PI");
    29.     expression.replace("abs(","Math.abs{");
    30.     expression.replace("sin(","Math.sin{");
    31.     expression.replace("cos(","Math.cos{");
    32.     expression.replace("tan","Math.tan");
    33.      //.... and so on for trigonometrical functions)
    34.  
    35.     expression.replace("sqrt","Math.sqrt");
    36.     expression.replace("(","[");
    37.     expression.replace(")","]");
    38.     expression.replace("^","POW");
    39.     expression.replace("+","PLUS");
    40.     expression.replace("-","MINUS");
    41.     expression.replace("*","MULT");
    42.     expression.replace("/","DIV");
    43.  
    44.      while (expression.contains("[")) //START SOLVING EXPRESSIONS BETWEEN BRACKETS
    45.      {
    46.  
    47.          QRegularExpression rep("\\[([^\\]]+)\\]");
    48.            QRegularExpressionMatch matchp = rep.match(expression);
    49.            QString expp_w_brackets = matchp.captured(0); //original expression with brakets
    50.            QString expp = matchp.captured(1);//expression without brakets
    51.  
    52.            while (expp.contains("POW")) //SOLVE POE EXPRESSION
    53.            {
    54.                QRegularExpression re1("(\\d+.\\d+POW)|(\\d+POW)");
    55.                QRegularExpressionMatch match1 = re1.match(expp);
    56.  
    57.                QRegularExpression re2("(POW\\d+.\\d+)|(POW\\d+)");
    58.                QRegularExpressionMatch match2 = re2.match(expp);
    59.  
    60.                if (match1.hasMatch())
    61.                {
    62.                    exp1 = match1.captured(0);
    63.                    exp1.replace("POW","");
    64.                }
    65.  
    66.                if (match2.hasMatch())
    67.                {
    68.                    exp2 = match2.captured(0);
    69.                    exp2.replace("POW","");
    70.                      }
    71.  
    72.                expp.replace (""+exp1+"" "POW"""+exp2+"" , "Math.pow(" ""+exp1+"" ","  ""+exp2+""  ")");
    73.            }
    74.  
    75.  
    76.            expp.replace ("PLUS","+");
    77.            expp.replace ("MINUS","-");
    78.            expp.replace("MULT","*");
    79.            expp.replace("DIV","/");
    80.  
    81.            QJSEngine parsexpressionp;
    82.            double resultp=parsexpressionp.evaluate(expp).toNumber();
    83.            QString BraketResult=(QString::number(resultp));
    84.            expression.replace(""+expp_w_brackets+"" ,""+BraketResult+"");
    85. }
    86.  
    87.     while (expression.contains("POW")) //SOLVE POE EXPRESSION
    88.     {
    89.         QRegularExpression re1("(\\d+.\\d+POW)|(\\d+POW)");
    90.         QRegularExpressionMatch match1 = re1.match(expression);
    91.  
    92.         QRegularExpression re2("(POW\\d+.\\d+)|(POW\\d+)");
    93.         QRegularExpressionMatch match2 = re2.match(expression);
    94.  
    95.  
    96.         if (match1.hasMatch())
    97.         {
    98.             exp1 = match1.captured(0);
    99.             exp1.replace("POW","");
    100.         }
    101.  
    102.         if (match2.hasMatch())
    103.         {
    104.             exp2 = match2.captured(0);
    105.             exp2.replace("POW","");
    106.               }
    107.  
    108.  
    109.         expression.replace (""+exp1+"" "POW"""+exp2+"" , "Math.pow(" ""+exp1+"" ","  ""+exp2+""  ")");
    110.      }
    111.  
    112.     expression.replace("{","(");
    113.     expression.replace("[","(");
    114.     expression.replace("]",")");
    115.     expression.replace ("PLUS","+");
    116.     expression.replace ("MINUS","-");
    117.     expression.replace("MULT","*");
    118.     expression.replace("DIV","/");
    119.     QJSEngine parsexpression;
    120.     double result=parsexpression.evaluate(expression).toNumber();
    121.     ui->Result->setText(QString::number(result));
    122. }
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    Last edited by sr1s; 8th May 2018 at 16:37.
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  6. 8th May 2018, 16:41 #6
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    Default Re: Parser for mathematic expression from QString

    Well, the more possibilities you add, the more difficult it will be to keep the code from getting ugly. At some point I think you may have to consider a recursive descent parser - you'll get into problems of precedence, embedded expressions (like "2^(6/3)"), etc. where the work of getting them suitable for the JS parser is as much as evaluating it yourself.

    Here is a simple one in C# which looks like it can be translated into C++ and modified pretty easily to support functions and precedence. Or you can go old-school and use Flex / Bison or Flex++ / Bison++. You'll learn more than you ever wanted to know about regular expressions.
    <=== The Great Pumpkin says ===>
    Please use CODE tags when posting source code so it is more readable. Click "Go Advanced" and then the "#" icon to insert the tags. Paste your code between them.
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