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MathParser.cs
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MathParser.cs
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using System;
using System.Collections.Generic;
using System.Globalization;
using System.Text;
namespace MathParserTK
{
#region Example usage
// public static void Main()
// {
// MathParser parser = new MathParser();
// string s1 = "pi+5*5+5*3-5*5-5*3+1E1";
// string s2 = "sin(cos(tg(sh(ch(th(100))))))";
// bool isRadians = false;
// double d1 = parser.Parse(s1, isRadians);
// double d2 = parser.Parse(s2, isRadians);
//
// Console.WriteLine(d1); // 13.141592...
// Console.WriteLine(d2); // 0.0174524023974442
// Console.ReadKey(true);
// }
#endregion
#region Common tips to extend this math parser
// If you want to add new operator, then add new item to supportedOperators
// dictionary and check next methods:
// (1) IsRightAssociated, (2) GetPriority, (3) SyntaxAnalysisRPN, (4) NumberOfArguments
//
// If you want to add new function, then add new item to supportedFunctions
// dictionary and check next above methods: (2), (3), (4).
//
// if you want to add new constant, then add new item to supportedConstants
#endregion
public class MathParser
{
#region Fields
#region Markers (each marker should have length equals to 1)
private const string NumberMaker = "#";
private const string OperatorMarker = "$";
private const string FunctionMarker = "@";
#endregion
#region Internal tokens
private const string Plus = OperatorMarker + "+";
private const string UnPlus = OperatorMarker + "un+";
private const string Minus = OperatorMarker + "-";
private const string UnMinus = OperatorMarker + "un-";
private const string Multiply = OperatorMarker + "*";
private const string Divide = OperatorMarker + "/";
private const string Degree = OperatorMarker + "^";
private const string LeftParent = OperatorMarker + "(";
private const string RightParent = OperatorMarker + ")";
private const string Sqrt = FunctionMarker + "sqrt";
private const string Sin = FunctionMarker + "sin";
private const string Cos = FunctionMarker + "cos";
private const string Tg = FunctionMarker + "tg";
private const string Ctg = FunctionMarker + "ctg";
private const string Sh = FunctionMarker + "sh";
private const string Ch = FunctionMarker + "ch";
private const string Th = FunctionMarker + "th";
private const string Log = FunctionMarker + "log";
private const string Ln = FunctionMarker + "ln";
private const string Exp = FunctionMarker + "exp";
private const string Abs = FunctionMarker + "abs";
#endregion
#region Dictionaries (containts supported input tokens, exclude number)
// Key -> supported input token, Value -> internal token or number
/// <summary>
/// Contains supported operators
/// </summary>
private readonly Dictionary<string, string> supportedOperators =
new Dictionary<string, string>
{
{ "+", Plus },
{ "-", Minus },
{ "*", Multiply },
{ "/", Divide },
{ "^", Degree },
{ "(", LeftParent },
{ ")", RightParent }
};
/// <summary>
/// Contains supported functions
/// </summary>
private readonly Dictionary<string, string> supportedFunctions =
new Dictionary<string, string>
{
{ "sqrt", Sqrt },
{ "√", Sqrt },
{ "sin", Sin },
{ "cos", Cos },
{ "tg", Tg },
{ "ctg", Ctg },
{ "sh", Sh },
{ "ch", Ch },
{ "th", Th },
{ "log", Log },
{ "exp", Exp },
{ "abs", Abs }
};
private readonly Dictionary<string, string> supportedConstants =
new Dictionary<string, string>
{
{"pi", NumberMaker + Math.PI.ToString() },
{"e", NumberMaker + Math.E.ToString() }
};
#endregion
#endregion
private readonly char decimalSeparator;
private bool isRadians;
#region Constructors
/// <summary>
/// Initialize new instance of MathParser
/// (symbol of decimal separator is read
/// from regional settings in system)
/// </summary>
public MathParser()
{
try
{
decimalSeparator = Char.Parse(System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NumberDecimalSeparator);
}
catch (FormatException ex)
{
throw new FormatException("Error: can't read char decimal separator from system, check your regional settings.", ex);
}
}
/// <summary>
/// Initialize new instance of MathParser
/// </summary>
/// <param name="decimalSeparator">Set decimal separator</param>
public MathParser(char decimalSeparator)
{
this.decimalSeparator = decimalSeparator;
}
#endregion
/// <summary>
/// Produce result of the given math expression
/// </summary>
/// <param name="expression">Math expression (infix/standard notation)</param>
/// <returns>Result</returns>
public double Parse(string expression, bool isRadians = true)
{
this.isRadians = isRadians;
try
{
return Calculate(ConvertToRPN(FormatString(expression)));
}
catch (DivideByZeroException e)
{
throw e;
}
catch (FormatException e)
{
throw e;
}
catch (InvalidOperationException e)
{
throw e;
}
catch (ArgumentOutOfRangeException e)
{
throw e;
}
catch (ArgumentException e)
{
throw e;
}
catch (Exception e)
{
throw e;
}
}
/// <summary>
/// Produce formatted string by the given string
/// </summary>
/// <param name="expression">Unformatted math expression</param>
/// <returns>Formatted math expression</returns>
private string FormatString(string expression)
{
if (string.IsNullOrEmpty(expression))
{
throw new ArgumentNullException("Expression is null or empty");
}
StringBuilder formattedString = new StringBuilder();
int balanceOfParenth = 0; // Check number of parenthesis
// Format string in one iteration and check number of parenthesis
// (this function do 2 tasks because performance priority)
for (int i = 0; i < expression.Length; i++)
{
char ch = expression[i];
if (ch == '(')
{
balanceOfParenth++;
}
else if (ch == ')')
{
balanceOfParenth--;
}
if (Char.IsWhiteSpace(ch))
{
continue;
}
else if (Char.IsUpper(ch))
{
formattedString.Append(Char.ToLower(ch));
}
else
{
formattedString.Append(ch);
}
}
if (balanceOfParenth != 0)
{
throw new FormatException("Number of left and right parenthesis is not equal");
}
return formattedString.ToString();
}
#region Convert to Reverse-Polish Notation
/// <summary>
/// Produce math expression in reverse polish notation
/// by the given string
/// </summary>
/// <param name="expression">Math expression in infix notation</param>
/// <returns>Math expression in postfix notation (RPN)</returns>
private string ConvertToRPN(string expression)
{
int pos = 0; // Current position of lexical analysis
StringBuilder outputString = new StringBuilder();
Stack<string> stack = new Stack<string>();
// While there is unhandled char in expression
while (pos < expression.Length)
{
string token = LexicalAnalysisInfixNotation(expression, ref pos);
outputString = SyntaxAnalysisInfixNotation(token, outputString, stack);
}
// Pop all elements from stack to output string
while (stack.Count > 0)
{
// There should be only operators
if (stack.Peek()[0] == OperatorMarker[0])
{
outputString.Append(stack.Pop());
}
else
{
throw new FormatException("Format exception,"
+ " there is function without parenthesis");
}
}
return outputString.ToString();
}
/// <summary>
/// Produce token by the given math expression
/// </summary>
/// <param name="expression">Math expression in infix notation</param>
/// <param name="pos">Current position in string for lexical analysis</param>
/// <returns>Token</returns>
private string LexicalAnalysisInfixNotation(string expression, ref int pos)
{
// Receive first char
StringBuilder token = new StringBuilder();
token.Append(expression[pos]);
// If it is a operator
if (supportedOperators.ContainsKey(token.ToString()))
{
// Determine it is unary or binary operator
bool isUnary = pos == 0 || "+-*/^(".Contains(expression[pos - 1].ToString());
pos++;
switch (token.ToString())
{
case "+":
return isUnary ? UnPlus : Plus;
case "-":
return isUnary ? UnMinus : Minus;
default:
return supportedOperators[token.ToString()];
}
}
else if (Char.IsLetter(token[0])
|| supportedFunctions.ContainsKey(token.ToString())
|| supportedConstants.ContainsKey(token.ToString()))
{
// Read function or constant name
while (++pos < expression.Length
&& Char.IsLetter(expression[pos]))
{
token.Append(expression[pos]);
}
if (supportedFunctions.ContainsKey(token.ToString()))
{
return supportedFunctions[token.ToString()];
}
else if (supportedConstants.ContainsKey(token.ToString()))
{
return supportedConstants[token.ToString()];
}
else
{
throw new ArgumentException("Unknown token");
}
}
else if (Char.IsDigit(token[0]) || token[0] == decimalSeparator)
{
// Read number
// Read the whole part of number
if (Char.IsDigit(token[0]))
{
while (++pos < expression.Length
&& Char.IsDigit(expression[pos]))
{
token.Append(expression[pos]);
}
}
else
{
// Because system decimal separator
// will be added below
token.Clear();
}
// Read the fractional part of number
if (pos < expression.Length
&& expression[pos] == decimalSeparator)
{
// Add current system specific decimal separator
token.Append(CultureInfo.CurrentCulture
.NumberFormat.NumberDecimalSeparator);
while (++pos < expression.Length
&& Char.IsDigit(expression[pos]))
{
token.Append(expression[pos]);
}
}
// Read scientific notation (suffix)
if (pos + 1 < expression.Length && expression[pos] == 'e'
&& (Char.IsDigit(expression[pos + 1])
|| (pos + 2 < expression.Length
&& (expression[pos + 1] == '+'
|| expression[pos + 1] == '-')
&& Char.IsDigit(expression[pos + 2]))))
{
token.Append(expression[pos++]); // e
if (expression[pos] == '+' || expression[pos] == '-')
token.Append(expression[pos++]); // sign
while (pos < expression.Length
&& Char.IsDigit(expression[pos]))
{
token.Append(expression[pos++]); // power
}
// Convert number from scientific notation to decimal notation
return NumberMaker + Convert.ToDouble(token.ToString());
}
return NumberMaker + token.ToString();
}
else
{
throw new ArgumentException("Unknown token in expression");
}
}
/// <summary>
/// Syntax analysis of infix notation
/// </summary>
/// <param name="token">Token</param>
/// <param name="outputString">Output string (math expression in RPN)</param>
/// <param name="stack">Stack which contains operators (or functions)</param>
/// <returns>Output string (math expression in RPN)</returns>
private StringBuilder SyntaxAnalysisInfixNotation(string token, StringBuilder outputString, Stack<string> stack)
{
// If it's a number just put to string
if (token[0] == NumberMaker[0])
{
outputString.Append(token);
}
else if (token[0] == FunctionMarker[0])
{
// if it's a function push to stack
stack.Push(token);
}
else if (token == LeftParent)
{
// If its '(' push to stack
stack.Push(token);
}
else if (token == RightParent)
{
// If its ')' pop elements from stack to output string
// until find the ')'
string elem;
while ((elem = stack.Pop()) != LeftParent)
{
outputString.Append(elem);
}
// if after this a function is in the peek of stack then put it to string
if (stack.Count > 0 &&
stack.Peek()[0] == FunctionMarker[0])
{
outputString.Append(stack.Pop());
}
}
else
{
// While priority of elements at peek of stack >= (>) token's priority
// put these elements to output string
while (stack.Count > 0 &&
Priority(token, stack.Peek()))
{
outputString.Append(stack.Pop());
}
stack.Push(token);
}
return outputString;
}
/// <summary>
/// Is priority of token less (or equal) to priority of p
/// </summary>
private bool Priority(string token, string p)
{
return IsRightAssociated(token) ?
GetPriority(token) < GetPriority(p) :
GetPriority(token) <= GetPriority(p);
}
/// <summary>
/// Is right associated operator
/// </summary>
private bool IsRightAssociated(string token)
{
return token == Degree;
}
/// <summary>
/// Get priority of operator
/// </summary>
private int GetPriority(string token)
{
switch (token)
{
case LeftParent:
return 0;
case Plus:
case Minus:
return 2;
case UnPlus:
case UnMinus:
return 6;
case Multiply:
case Divide:
return 4;
case Degree:
case Sqrt:
return 8;
case Sin:
case Cos:
case Tg:
case Ctg:
case Sh:
case Ch:
case Th:
case Log:
case Ln:
case Exp:
case Abs:
return 10;
default:
throw new ArgumentException("Unknown operator");
}
}
#endregion
#region Calculate expression in RPN
/// <summary>
/// Calculate expression in reverse-polish notation
/// </summary>
/// <param name="expression">Math expression in reverse-polish notation</param>
/// <returns>Result</returns>
private double Calculate(string expression)
{
int pos = 0; // Current position of lexical analysis
var stack = new Stack<double>(); // Contains operands
// Analyse entire expression
while (pos < expression.Length)
{
string token = LexicalAnalysisRPN(expression, ref pos);
stack = SyntaxAnalysisRPN(stack, token);
}
// At end of analysis in stack should be only one operand (result)
if (stack.Count > 1)
{
throw new ArgumentException("Excess operand");
}
return stack.Pop();
}
/// <summary>
/// Produce token by the given math expression
/// </summary>
/// <param name="expression">Math expression in reverse-polish notation</param>
/// <param name="pos">Current position of lexical analysis</param>
/// <returns>Token</returns>
private string LexicalAnalysisRPN(string expression, ref int pos)
{
StringBuilder token = new StringBuilder();
// Read token from marker to next marker
token.Append(expression[pos++]);
while (pos < expression.Length && expression[pos] != NumberMaker[0]
&& expression[pos] != OperatorMarker[0]
&& expression[pos] != FunctionMarker[0])
{
token.Append(expression[pos++]);
}
return token.ToString();
}
/// <summary>
/// Syntax analysis of reverse-polish notation
/// </summary>
/// <param name="stack">Stack which contains operands</param>
/// <param name="token">Token</param>
/// <returns>Stack which contains operands</returns>
private Stack<double> SyntaxAnalysisRPN(Stack<double> stack, string token)
{
// if it's operand then just push it to stack
if (token[0] == NumberMaker[0])
{
stack.Push(double.Parse(token.Remove(0, 1)));
}
// Otherwise apply operator or function to elements in stack
else if (NumberOfArguments(token) == 1)
{
double arg = stack.Pop();
double rst;
switch (token)
{
case UnPlus:
rst = arg;
break;
case UnMinus:
rst = -arg;
break;
case Sqrt:
rst = Math.Sqrt(arg);
break;
case Sin:
rst = ApplyTrigFunction(Math.Sin, arg);
break;
case Cos:
rst = ApplyTrigFunction(Math.Cos, arg);
break;
case Tg:
rst = ApplyTrigFunction(Math.Tan, arg);
break;
case Ctg:
rst = 1 / ApplyTrigFunction(Math.Tan, arg);
break;
case Sh:
rst = Math.Sinh(arg);
break;
case Ch:rst =
rst = Math.Cosh(arg);
break;
case Th:
rst = Math.Tanh(arg);
break;
case Ln:
rst = Math.Log(arg);
break;
case Exp:
rst = Math.Exp(arg);
break;
case Abs:
rst = Math.Abs(arg);
break;
default:
throw new ArgumentException("Unknown operator");
}
stack.Push(rst);
}
else
{
// otherwise operator's number of arguments equals to 2
double arg2 = stack.Pop();
double arg1 = stack.Pop();
double rst;
switch (token)
{
case Plus:
rst = arg1 + arg2;
break;
case Minus:
rst = arg1 - arg2;
break;
case Multiply:
rst = arg1 * arg2;
break;
case Divide:
if (arg2 == 0)
{
throw new DivideByZeroException("Second argument is zero");
}
rst = arg1 / arg2;
break;
case Degree:
rst = Math.Pow(arg1, arg2);
break;
case Log:
rst = Math.Log(arg2, arg1);
break;
default:
throw new ArgumentException("Unknown operator");
}
stack.Push(rst);
}
return stack;
}
/// <summary>
/// Apply trigonometric function
/// </summary>
/// <param name="func">Trigonometric function</param>
/// <param name="arg">Argument</param>
/// <returns>Result of function</returns>
private double ApplyTrigFunction(Func<double, double> func, double arg)
{
if (!isRadians)
{
arg = arg * Math.PI / 180; // Convert value to degree
}
return func(arg);
}
/// <summary>
/// Produce number of arguments for the given operator
/// </summary>
private int NumberOfArguments(string token)
{
switch (token)
{
case UnPlus:
case UnMinus:
case Sqrt:
case Tg:
case Sh:
case Ch:
case Th:
case Ln:
case Ctg:
case Sin:
case Cos:
case Exp:
case Abs:
return 1;
case Plus:
case Minus:
case Multiply:
case Divide:
case Degree:
case Log:
return 2;
default:
throw new ArgumentException("Unknown operator");
}
}
#endregion
}
}