lexer.js

var Mexp=require('./math_function.js');
	function inc(arr,val){
		for(var i=0;i<arr.length;i++)
			arr[i]+=val;
		return arr;
	}
	var token=['sin','cos','tan','pi','(',')','P','C',
		  'asin','acos','atan','7','8','9','int',
		  'cosh','acosh','ln','^','root','4','5','6','/','!',
		  'tanh','atanh','Mod','1','2','3','*',
		  'sinh','asinh','e','log','0','.','+','-',',','Sigma','n','Pi','pow'];
	var show=['sin','cos','tan','&pi;','(',')','P','C',
		'asin','acos','atan','7','8','9','Int',
		'cosh','acosh',' ln','^','root','4','5','6','&divide;','!',
		'tanh','atanh',' Mod ','1','2','3','&times;',
		'sinh','asinh','e',' log','0','.','+','-',',','&Sigma;','n','&Pi;','pow'];
	var eva=[Mexp.math.sin,Mexp.math.cos,Mexp.math.tan,'PI','(',')',Mexp.math.P,Mexp.math.C,
		Mexp.math.asin,Mexp.math.acos,Mexp.math.atan,'7','8','9',Math.floor,
		Mexp.math.cosh,Mexp.math.acosh,Math.log,Math.pow,Math.sqrt,'4','5','6',Mexp.math.div,Mexp.math.fact,
		Mexp.math.tanh,Mexp.math.atanh,Mexp.math.mod,'1','2','3',Mexp.math.mul,
		Mexp.math.sinh,Mexp.math.asinh,'E',Mexp.math.log,'0','.',Mexp.math.add,Mexp.math.sub,',',Mexp.math.sigma,'n',Mexp.math.Pi,Math.pow];
	var preced={0:11,1:0,2:3,3:0,4:0,5:0,6:0,7:11,8:11,9:1,10:10,11:0,12:11,13:0};
	var type=[0,0,0,3,4,5,10,10,
		0,0,0,1,1,1,0,
		0,0,0,10,0,1,1,1,2,7,
		0,0,2,1,1,1,2,
		0,0,3,0,1,6,9,9,11,12,13,12,8];
	 /*
	0 : function with syntax function_name(Maths_exp)
	1 : numbers
	2 : binary operators like * / Mod left associate and same precedence
	3 : Math constant values like e,pi,Cruncher ans
	4 : opening bracket
	5 : closing bracket
	6 : decimal
	7 : function with syntax (Math_exp)function_name
	8: function with syntax function_name(Math_exp1,Math_exp2)
	9 : binary operator like +,-
	10: binary operator like P C or ^
	11: ,
	12: function with , seperated three parameters
	13: variable of Sigma function
	 */
	var type0={0:true,1:true,3:true,4:true,6:true,8:true,9:true,12:true,13:true},//type2:true,type4:true,type9:true,type11:true,type21:true,type22
	type1={0:true,1:true,2:true,3:true,4:true,5:true,6:true,7:true,8:true,9:true,10:true,11:true,12:true,13:true},//type3:true,type5:true,type7:true,type23
	type_1={0:true,3:true,4:true,8:true,12:true,13:true},
	empty={},
	type_3={0:true,1:true,3:true,4:true,6:true,8:true,12:true,13:true},//type_5:true,type_7:true,type_23
	type6={1:true},
	newAr=[[],
			["1","2","3","7","8","9","4","5","6","+","-","*","/","(",")","^","!","P","C","e","0",".",",","n"],
			["pi","ln","Pi"],
			["sin","cos","tan","Del","int","Mod","log","pow"],
			["asin","acos","atan","cosh","root","tanh","sinh"],
			["acosh","atanh","asinh","Sigma"]];
	function match(str1,str2,i,x){
		for(var f=0;f<x;f++){
			if (str1[i+f]!==str2[f])
				return false;
		}
		return true;
	}
	Mexp.addToken=function(tokens){
		for(i=0;i<tokens.length;i++){
			x=tokens[i].token.length;
			var temp=-1;

			//newAr is a specially designed data structure in which 1D array at location one of 2d array has all string with length 1 2 with 2 and so on

			if (x<newAr.length)	//match to check if token is really huge and not existing
								//if not checked it will break in next line as undefined index
				for(y=0;y<newAr[x].length;y++){
					if (tokens[i].token===newAr[x][y]){
						temp=token.indexOf(newAr[x][y]);
						break;
					}
				}
			if (temp===-1) {
				token.push(tokens[i].token);
				type.push(tokens[i].type);
				if(newAr.length<=tokens[i].token.length)
					newAr[tokens[i].token.length]=[];
				newAr[tokens[i].token.length].push(tokens[i].token);
				eva.push(tokens[i].value);
				show.push(tokens[i].show);
			}
			else {
				token[temp]=tokens[i].token;
				type[temp]=tokens[i].type;
				eva[temp]=tokens[i].value;
				show[temp]=tokens[i].show;
			}
		}
	};
	Mexp.lex=function(inp,tokens){
		'use strict';
		var str=[{type:4,value:"(",show:"(",pre:0}];
		var ptc=[];	//Parenthesis to close at the beginning is after one token
		var inpStr=inp;
		var key;
        var pcounter=0;
		var allowed=type0;
		var bracToClose=0;
		var asterick=empty;
		var prevKey='';
		var i,x,y;
		if(typeof tokens!=="undefined")
			Mexp.addToken(tokens);
		var obj={};
		for(i=0;i<inpStr.length;i++){
			if (inpStr[i]==' ') {
				continue;
			}
			key='';
			sec:for(x=(inpStr.length-i>(newAr.length-2)?newAr.length-1:inpStr.length-i);x>0;x--){
				for(y=0;y<newAr[x].length;y++){
					if (match(inpStr,newAr[x][y],i,x)){
						key=newAr[x][y];
						break sec;
					}
				}
			}
			i+=key.length-1;
			if(key===''){
				throw(new Mexp.exception("Can't understand after "+inpStr.slice(i)));
			}
			var index=token.indexOf(key);
			var cToken=key;
			var cType=type[index];
			var cEv=eva[index];
			var cPre=preced[cType];
			var	cShow=show[index];
			var pre=str[str.length-1];
			for(j=ptc.length;j--;){	//loop over ptc
				if(ptc[j]===0){
					if([0,2,3,5,9,11,12,13].indexOf(cType)!==-1){
						if(allowed[cType]!==true){
							throw(new Mexp.exception(key+" is not allowed after "+prevKey));
						}
						str.push({value:")",type:5,pre:0,show:")"});
						allowed=type1;
						asterick=type_3;
						inc(ptc,-1).pop();
					}
				}
			}
			if(allowed[cType]!==true){
				throw(new Mexp.exception(key+" is not allowed after "+prevKey));
			}
			if(asterick[cType]===true){
				cType=2;
				cEv=Mexp.math.mul;
				cShow="&times;";
				cPre=3;
				i=i-key.length;
		 	}
			obj={value:cEv,type:cType,pre:cPre,show:cShow};
			if(cType===0){
				allowed=type0;
				asterick=empty;
				inc(ptc,2).push(2);
				str.push(obj);
				str.push({value:"(",type:4,pre:0,show:"("});
			}
			else if(cType===1){
				if(pre.type===1){
					pre.value+=cEv;
					inc(ptc,1);
				}
				else {
					str.push(obj);
				}
				allowed=type1;
				asterick=type_1;
			}
			else if(cType===2){
				allowed=type0;
				asterick=empty;
				inc(ptc,2);
				str.push(obj);
			}
			else if(cType===3){//constant
				str.push(obj);
				allowed=type1;
				asterick=type_3;
			}
			else if(cType===4){
                pcounter+=ptc.length;
                ptc=[];
				bracToClose++;
				allowed=type0;
				asterick=empty;
				str.push(obj);
			}
			else if(cType===5){
				if(!bracToClose){
					throw(new Mexp.exception("Closing parenthesis are more than opening one, wait What!!!"));
				}
                while(pcounter--){	//loop over ptc
    						str.push({value:")",type:5,pre:0,show:")"});
    			}
                pcounter=0;
				bracToClose--;
				allowed=type1;
				asterick=type_3;
				str.push(obj);
			}
			else if(cType===6){
				if(pre.hasDec){
					throw(new Mexp.exception("Two decimals are not allowed in one number"));
				}
				if(pre.type!==1){
					pre={value:0,type:1,pre:0};	//pre needs to be changed as it will the last value now to be safe in later code
					str.push(pre);
					inc(ptc,-1);
				}
				allowed=type6;
				inc(ptc,1);
				asterick=empty;
				pre.value+=cEv;
				pre.hasDec=true;
			}
			else if(cType===7){
				allowed=type1;
				asterick=type_3;
				inc(ptc,1);
				str.push(obj);
			}
			if(cType===8){
				allowed=type0;
				asterick=empty;
				inc(ptc,4).push(4);
				str.push(obj);
				str.push({value:"(",type:4,pre:0,show:"("});
			}
			else if(cType===9){
				if(pre.type===9){
					if(pre.value===Mexp.math.add){
						pre.value=cEv;
						pre.show=cShow;
						inc(ptc,1);
					}
					else if(pre.value===Mexp.math.sub&&cShow==='-'){
						pre.value=Mexp.math.add;
						pre.show='+';
						inc(ptc,1);
					}
				}
				else if(pre.type!==5&&pre.type!==7&&pre.type!==1&&pre.type!==3&&pre.type!==13){//changesign only when negative is found
					if(cToken==='-'){//do nothing for + token
									//don't add with the above if statement as that will run the else statement of parent if on Ctoken +
						allowed=type0;
						asterick=empty;
						inc(ptc,2).push(2);
						str.push({value:Mexp.math.changeSign,type:0,pre:21,show:"-"});
						str.push({value:"(",type:4,pre:0,show:"("});
					}
				}
				else{
					str.push(obj);
					inc(ptc,2);
				}
				allowed=type0;
				asterick=empty;
			}
			else if(cType===10){
				allowed=type0;
				asterick=empty;
				inc(ptc,2);
				str.push(obj);
			}
			else if(cType===11){
				allowed=type0;
				asterick=empty;
				str.push(obj);
			}
			else if(cType===12){
				allowed=type0;
				asterick=empty;
				inc(ptc,6).push(6);
				str.push(obj);
				str.push({value:"(",type:4,pre:0});
			}
			else if(cType===13){
				allowed=type1;
				asterick=type_3;
				str.push(obj);
			}
			inc(ptc,-1);
			prevKey=key;
		}
		for(var j=ptc.length;j--;){	//loop over ptc
			if(ptc[j]===0){

				str.push({value:")",show:")",type:5,pre:3});
				inc(ptc,-1).pop();
			}
		}
		if (allowed[5]!==true) {
			throw(new Mexp.exception("complete the expression"));
		}
		while(bracToClose--)
			str.push({value:")",show:")",type:5,pre:3});

		str.push({type:5,value:")",show:")",pre:0});
//        console.log(str);
		return new Mexp(str);
	};
    module.exports=Mexp;