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Posted 19 Sep 2012
Licenced CPOL

Yet Another Math Parser (YAMP)

, 30 Sep 2012
Constructing a fast math parser using Reflection to do numerics like Matlab.
YAMP
YAMPCompare
LLMathParser
MathFormula
MathParser
MathParserNet
Exceptions
MathParserTK
YAMPCompare.pidb
YAMPConsole
YAMPConsole.pidb
Exceptions
Expressions
Functions
ArgumentFunctions
LinearAlgebra
LogicFunctions
Spectroscopy
StandardFunctions
Trigonometric
Interfaces
Numerics
Decompositions
Integration
Interpolations
ODE
Optimization
Others
Solvers
Operators
AssigmentOperators
BinaryOperators
DotOperators
LogicOperators
UnaryOperators
Values
YAMP.csproj.user
YAMP.pidb
YAMP.csproj.user
YAMP.pidb
/* Copyright (C) 2005 <Paratrooper> paratrooper666@gmx.net
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  any later version.
 */

using System;
using System.Collections;
using System.Text.RegularExpressions;

namespace MathParser
{
	public enum Mode { RAD, DEG, GRAD };

	public class Parser
	{
		private ArrayList FunctionList = new ArrayList( new string[] { "abs", "acos", "asin", "atan", "ceil", "cos", "cosh", "exp", "floor", "ln", "log", "sign", "sin", "sinh", "sqrt", "tan", "tanh" } );
		private double Value;
		private double Factor;
		private Mode mode;

		// Constructor
		public Parser()
		{
			this.Mode = Mode.RAD;
		}
		public Parser( Mode mode )
		{
			this.Mode  = mode;
		}

		// Getter & Setter
		public double Result
		{
			get{ return this.Value; }
		}
		public Mode Mode
		{
			get{ return this.mode; }
			set
			{
				this.mode = value;
				switch( value )
				{
					case Mode.RAD :
						this.Factor = 1.0;
						break;
					case Mode.DEG :
						this.Factor = 2.0 * Math.PI / 360.0;
						break;
					case Mode.GRAD :
						this.Factor = 2.0 * Math.PI / 400.0;
						break;
				}
			}
		}

		public bool Evaluate( string Expression ) 
		{
			try 
			{
				// ****************************************************************************************
				// ** MathParser in action:                                                              **
				// ** Expression = "-(5 - 10)^(-1)  ( 3 + 2(    cos( 3 Pi )+( 2+ ln( exp(1) ) )    ^3))" **
				// ****************************************************************************************
				//
				//
				// ----------
				// - Step 1 -
				// ----------
				// Remove blank.
				//
				// -(5 - 10)^(-1)  ( 3 + 2(    cos( 3 Pi )+( 2+ ln( exp(1) ) )    ^3)) -> -(5-10)^(-1)(3+2(cos(3Pi)+(2+ln(exp(1)))^3))
				//
				Expression = Expression.Replace( " ", "" );
				//
				// ----------
				// - Step 2 -
				// ----------
				// Insert '*' if necessary.
				//
				//                                                             _    _      _
				// -(5-10)^(-1)(3+2(cos(3Pi)+(2+ln(exp(1)))^3)) -> -(5-10)^(-1)*(3+2*(cos(3*Pi)+(2+ln(exp(1)))^3))
				//             |   |     |
				//
				Regex regEx = new Regex( @"(?<=[\d\)])(?=[a-df-z\(])|(?<=pi)(?=[^\+\-\*\/\\^!)])|(?<=\))(?=\d)|(?<=[^\/\*\+\-])(?=exp)", RegexOptions.IgnoreCase );
				Expression = regEx.Replace( Expression, "*" );
				//
				// ----------
				// - Step 3 -
				// ----------
				// Replace constants: Pi -> 3,14...
				//
				//                                                                        ____
				// -(5-10)^(-1)*(3+2*(cos(3*Pi)+(2+ln(e))^3)) -> -(5-10)^(-1)*(3+2*(cos(3*3,14)+(2+ln(exp(1)))^3))
				//                          --
				//
				regEx = new Regex( "pi", RegexOptions.IgnoreCase );
				Expression = regEx.Replace( Expression, Math.PI.ToString() );
				//
				// ----------
				// - Step 4 -
				// ----------
				// Search for parentheses an solve the expression between it.
				//
				//                                                       _____
				// -(5-10)^(-1)*(3+2*(cos(3*3,14)+(2+ln(exp(1)))^3)) -> -{-5}^(-1)*(3+2*(cos(3*3,14)+(2+ln(exp(1)))^3))
				//  |_____|
				//                                                          __
				// -{-5}^(-1)*(3+2*(cos(3*3,14)+(2+ln(exp(1)))^3)) -> -{-5}^-1*(3+2*(cos(3*3,14)+(2+ln(exp(1)))^3))
				//       |__|
				//                                                                    ____
				// -{-5}^-1*(3+2*(cos(3*3,14)+(2+ln(exp(1)))^3)) -> -{-5}^-1*(3+2*(cos9,42+(2+ln(exp(1)))^3))
				//                   |______|
				//                                                                              _
				// -{-5}^-1*(3+2*(cos9,72+(2+ln(exp(1)))^3)) -> -{-5}^-1*(3+2*(cos9,72+(2+ln(exp1))^3))
				//                                 |_|
				//                                                                        ____
				// -{-5}^-1*(3+2*(cos9,72+(2+ln(exp1))^3)) -> -{-5}^-1*(3+2*(cos9,72+(2+ln2,71)^3))
				//                             |____|
				//                                                                 ____
				// -{-5}^-1*(3+2*(cos9,72+(2+ln2,71)^3)) -> -{-5}^-1*(3+2*(cos9,72+{3}^3))
				//                        |_________|
				//                                                 __
				// -{-5}^-1*(3+2*(cos9,72+{3}^3)) -> -{-5}^-1*(3+2*26)
				//               |_____________|
				//                               __
				// -{-5}^-1*(3+2*26) -> -{-5}^-1*55
				//          |______|
				//
				regEx = new Regex( @"([a-z]*)\(([^\(\)]+)\)(\^|!?)", RegexOptions.IgnoreCase );
				Match m = regEx.Match( Expression );
				while( m.Success )
				{
					if( m.Groups[3].Value.Length > 0 ) Expression = Expression.Replace( m.Value, "{" + m.Groups[1].Value + this.Solve( m.Groups[2].Value ) + "}" + m.Groups[3].Value );
					else Expression = Expression.Replace( m.Value, m.Groups[1].Value + this.Solve( m.Groups[2].Value ) );
					m = regEx.Match( Expression );
				}
				//
				// ----------
				// - Step 5 -
				// ----------
				// There are no more parentheses. Solve the expression and convert it to double.
				//                __
				// -{-5}^-1*55 => 11
				// |_________|
				//
				this.Value = Convert.ToDouble( this.Solve( Expression ) );
				return true;
			}
			catch
			{
				// Shit!
				return false;
			}
		}

		private string Solve( string Expression )
		{
			// Solve Sin, Cos, Tan...
			Regex regEx = new Regex( @"([a-z]{2,})([\+-]?\d+,*\d*[eE][\+-]*\d+|[\+-]?\d+,*\d*)", RegexOptions.IgnoreCase );
			Match m = regEx.Match( Expression );
			while( m.Success && this.FunctionList.IndexOf(m.Groups[1].Value.ToLower() ) > -1  )
			{
				switch( m.Groups[1].Value.ToLower() )
				{
					case "abs" :
						Expression = Expression.Replace( m.Groups[0].Value, Math.Abs( Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
						m = regEx.Match( Expression );
						continue;
					case "acos" :
						Expression = Expression.Replace( m.Groups[0].Value , Math.Acos( this.Factor * Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
						m = regEx.Match( Expression );
						continue;
					case "asin" :
						Expression = Expression.Replace( m.Groups[0].Value , Math.Asin( this.Factor * Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
						m = regEx.Match( Expression );
						continue;
					case "atan" :
						Expression = Expression.Replace( m.Groups[0].Value , Math.Atan( this.Factor * Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
						m = regEx.Match( Expression );
						continue;
					case "cos" :
						Expression = Expression.Replace( m.Groups[0].Value , Math.Cos( this.Factor * Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
						m = regEx.Match( Expression );
						continue;
					case "ceil" :
						Expression = Expression.Replace( m.Groups[0].Value , Math.Ceiling( Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
						m = regEx.Match( Expression );
						continue;
					case "cosh" :
						Expression = Expression.Replace( m.Groups[0].Value , Math.Cosh( this.Factor * Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
						m = regEx.Match( Expression );
						continue;
					case "exp" :
						Expression = Expression.Replace( m.Groups[0].Value , Math.Exp( Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
						m = regEx.Match( Expression );
						continue;
					case "floor" :
						Expression = Expression.Replace( m.Groups[0].Value , Math.Floor( Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
						m = regEx.Match( Expression );
						continue;
					case "ln" :
						Expression = Expression.Replace( m.Groups[0].Value , Math.Log( Convert.ToDouble( m.Groups[2].Value ), Math.Exp(1.0) ).ToString() );
						m = regEx.Match( Expression );
						continue;
					case "log" :
						Expression = Expression.Replace( m.Groups[0].Value , Math.Log10( Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
						m = regEx.Match( Expression );
						continue;
					case "sign" :
						Expression = Expression.Replace( m.Groups[0].Value , Math.Sign( Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
						m = regEx.Match( Expression );
						continue;
					case "sin" :
						Expression = Expression.Replace( m.Groups[0].Value , Math.Sin( this.Factor * Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
						m = regEx.Match( Expression );
						continue;
					case "sinh" :
						Expression = Expression.Replace( m.Groups[0].Value , Math.Sinh( this.Factor * Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
						m = regEx.Match( Expression );
						continue;
					case "sqrt" :
						Expression = Expression.Replace( m.Groups[0].Value , Math.Sqrt( Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
						m = regEx.Match( Expression );
						continue;
					case "tan" :
						Expression = Expression.Replace( m.Groups[0].Value , Math.Tan( this.Factor * Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
						m = regEx.Match( Expression );
						continue;
					case "tanh" :
						Expression = Expression.Replace( m.Groups[0].Value , Math.Tanh( this.Factor * Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
						m = regEx.Match( Expression );
						continue;
				}
			}
			// Solve Factorial.
			regEx = new Regex( @"\{(.+)\}!" ); // Search for patterns like {5}!
			m = regEx.Match( Expression );
			while( m.Success )
			{
				double n = Convert.ToDouble( m.Groups[1].Value );
				if( (n < 0) && (n != Math.Round(n)) ) throw new Exception(); // Value negative or not integer -> throw exception
				Expression = regEx.Replace( Expression, this.Fact( Convert.ToDouble( m.Groups[1].Value ) ).ToString(), 1 );
				m = regEx.Match( Expression );
			}
			regEx = new Regex( @"(\d+,*\d*[eE][\+-]?\d+|\d+,*\d*)!" ); // Search for patterns like 5!
			m = regEx.Match( Expression );
			while( m.Success )
			{
				double n = Convert.ToDouble( m.Groups[1].Value );
				if( (n < 0) && (n != Math.Round(n)) ) throw new Exception(); // Value negative or not integer -> throw exception
				Expression = regEx.Replace( Expression, this.Fact( Convert.ToDouble( m.Groups[1].Value ) ).ToString(), 1 );
				m = regEx.Match( Expression ); 
			}
			// Solve power.
			regEx = new Regex( @"\{(.+)\}\^(-?\d+,*\d*[eE][\+-]?\d+|-?\d+,*\d*)" ); // Search for patterns like {-5}^-1
			m = regEx.Match( Expression, 0 );
			while( m.Success )
			{
				Expression = Expression.Replace( m.Value, Math.Pow( Convert.ToDouble( m.Groups[1].Value ), Convert.ToDouble( m.Groups[2].Value ) ).ToString() );
				m = regEx.Match( Expression );
			}
			regEx = new Regex( @"(\d+,*\d*e[\+-]?\d+|\d+,*\d*)\^(-?\d+,*\d*[eE][\+-]?\d+|-?\d+,*\d*)" ); // Search for patterns like 5^-1
			m = regEx.Match( Expression, 0 );
			while( m.Success )
			{
				Expression = regEx.Replace( Expression, Math.Pow( Convert.ToDouble( m.Groups[1].Value ), Convert.ToDouble( m.Groups[2].Value ) ).ToString(), 1 );
				m = regEx.Match( Expression );
			}
			// Solve multiplication / division.
			regEx = new Regex( @"([\+-]?\d+,*\d*[eE][\+-]?\d+|[\-\+]?\d+,*\d*)([\/\*])(-?\d+,*\d*[eE][\+-]?\d+|-?\d+,*\d*)" );
			m = regEx.Match( Expression, 0 );
			while( m.Success )
			{
				double result;
				switch( m.Groups[2].Value )
				{
					case "*" :
						result = Convert.ToDouble( m.Groups[1].Value ) * Convert.ToDouble( m.Groups[3].Value );
						if( (result < 0) || (m.Index == 0) ) Expression = regEx.Replace( Expression, result.ToString(), 1 );
						else Expression = Expression.Replace( m.Value, "+" + result );
						m = regEx.Match( Expression );
						continue;
					case "/" :
						result = Convert.ToDouble( m.Groups[1].Value ) / Convert.ToDouble( m.Groups[3].Value );
						if( (result < 0) || (m.Index == 0) ) Expression = regEx.Replace( Expression, result.ToString(), 1 );
						else Expression = regEx.Replace( Expression, "+" + result, 1 );
						m = regEx.Match( Expression );
						continue;
				}
			}
			// Solve addition / subtraction.
			regEx = new Regex( @"([\+-]?\d+,*\d*[eE][\+-]?\d+|[\+-]?\d+,*\d*)([\+-])(-?\d+,*\d*[eE][\+-]?\d+|-?\d+,*\d*)" );
			m = regEx.Match( Expression, 0 );
			while( m.Success )
			{
				double result;
				switch( m.Groups[2].Value )
				{
					case "+" :
						result = Convert.ToDouble( m.Groups[1].Value ) + Convert.ToDouble( m.Groups[3].Value );
						if( (result < 0) || (m.Index == 0) ) Expression = regEx.Replace( Expression, result.ToString(), 1 );
						else Expression = regEx.Replace( Expression, "+" + result, 1 );
						m = regEx.Match( Expression );
						continue;
					case "-" :
						result = Convert.ToDouble( m.Groups[1].Value ) - Convert.ToDouble( m.Groups[3].Value );
						if( (result < 0) || (m.Index == 0) ) Expression = regEx.Replace( Expression, result.ToString(), 1 );
						else Expression = regEx.Replace( Expression, "+" + result, 1 );
						m = regEx.Match( Expression );
						continue;
				}
			}
			if( Expression.StartsWith( "--" ) ) Expression = Expression.Substring(2);
			return Expression;
		}

		// Calculate Factorial.
		private double Fact( double n )
		{
			return n == 0.0 ? 1.0 : n * Fact( n - 1.0 );
		}
	}
}

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About the Author

Florian Rappl
Architect
Germany Germany
Florian lives in Munich, Germany. He started his programming career with Perl. After programming C/C++ for some years he discovered his favorite programming language C#. He did work at Siemens as a programmer until he decided to study Physics.

During his studies he worked as an IT consultant for various companies. After graduating with a PhD in theoretical particle Physics he is working as a senior technical consultant in the field of home automation and IoT.

Florian has been giving lectures in C#, HTML5 with CSS3 and JavaScript, software design, and other topics. He is regularly giving talks at user groups, conferences, and companies. He is actively contributing to open-source projects. Florian is the maintainer of AngleSharp, a completely managed browser engine.

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