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- 'use strict'
- var Mexp = require('./math_function.js')
- function inc(arr, val) {
- for (var i = 0; i < arr.length; i++) {
- arr[i] += val
- }
- return arr
- }
- var tokens = [
- { token: 'sin', show: 'sin', type: 0, value: Mexp.math.sin },
- { token: 'cos', show: 'cos', type: 0, value: Mexp.math.cos },
- { token: 'tan', show: 'tan', type: 0, value: Mexp.math.tan },
- { token: 'pi', show: 'π', type: 3, value: 'PI' },
- { token: '(', show: '(', type: 4, value: '(' },
- { token: ')', show: ')', type: 5, value: ')' },
- { token: 'P', show: 'P', type: 10, value: Mexp.math.P },
- { token: 'C', show: 'C', type: 10, value: Mexp.math.C },
- { token: ' ', show: ' ', type: 14, value: ' '.anchor },
- { token: 'asin', show: 'asin', type: 0, value: Mexp.math.asin },
- { token: 'acos', show: 'acos', type: 0, value: Mexp.math.acos },
- { token: 'atan', show: 'atan', type: 0, value: Mexp.math.atan },
- { token: '7', show: '7', type: 1, value: '7' },
- { token: '8', show: '8', type: 1, value: '8' },
- { token: '9', show: '9', type: 1, value: '9' },
- { token: 'int', show: 'Int', type: 0, value: Math.floor },
- { token: 'cosh', show: 'cosh', type: 0, value: Mexp.math.cosh },
- { token: 'acosh', show: 'acosh', type: 0, value: Mexp.math.acosh },
- { token: 'ln', show: ' ln', type: 0, value: Math.log },
- { token: '^', show: '^', type: 10, value: Math.pow },
- { token: 'root', show: 'root', type: 0, value: Math.sqrt },
- { token: '4', show: '4', type: 1, value: '4' },
- { token: '5', show: '5', type: 1, value: '5' },
- { token: '6', show: '6', type: 1, value: '6' },
- { token: '/', show: '÷', type: 2, value: Mexp.math.div },
- { token: '!', show: '!', type: 7, value: Mexp.math.fact },
- { token: 'tanh', show: 'tanh', type: 0, value: Mexp.math.tanh },
- { token: 'atanh', show: 'atanh', type: 0, value: Mexp.math.atanh },
- { token: 'Mod', show: ' Mod ', type: 2, value: Mexp.math.mod },
- { token: '1', show: '1', type: 1, value: '1' },
- { token: '2', show: '2', type: 1, value: '2' },
- { token: '3', show: '3', type: 1, value: '3' },
- { token: '*', show: '×', type: 2, value: Mexp.math.mul },
- { token: 'sinh', show: 'sinh', type: 0, value: Mexp.math.sinh },
- { token: 'asinh', show: 'asinh', type: 0, value: Mexp.math.asinh },
- { token: 'e', show: 'e', type: 3, value: 'E' },
- { token: 'log', show: ' log', type: 0, value: Mexp.math.log },
- { token: '0', show: '0', type: 1, value: '0' },
- { token: '.', show: '.', type: 6, value: '.' },
- { token: '+', show: '+', type: 9, value: Mexp.math.add },
- { token: '-', show: '-', type: 9, value: Mexp.math.sub },
- { token: ',', show: ',', type: 11, value: ',' },
- { token: 'Sigma', show: 'Σ', type: 12, value: Mexp.math.sigma },
- { token: 'n', show: 'n', type: 13, value: 'n' },
- { token: 'Pi', show: 'Π', type: 12, value: Mexp.math.Pi },
- { token: 'pow', show: 'pow', type: 8, value: Math.pow, numberOfArguments: 2 },
- { token: '&', show: '&', type: 9, value: Mexp.math.and },
- ]
- 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,
- 14: -1,
- 15: 11, // will be filtered after lexer
- } // stores precedence by types
- for (var i = 0; i < tokens.length; i++) {
- tokens[i].precedence = preced[tokens[i].type]
- }
- var type0 = {
- 0: true,
- 1: true,
- 3: true,
- 4: true,
- 6: true,
- 8: true,
- 9: true,
- 12: true,
- 13: true,
- 14: true,
- 15: true,
- } // type2:true,type4:true,type9:true,type11:true,type21:true,type22
- var 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,
- 15: true,
- } // type3:true,type5:true,type7:true,type23
- var type1Asterick = {
- 0: true,
- 3: true,
- 4: true,
- 8: true,
- 12: true,
- 13: true,
- 15: true,
- }
- var empty = {}
- var type3Asterick = {
- 0: true,
- 1: true,
- 3: true,
- 4: true,
- 6: true,
- 8: true,
- 12: true,
- 13: true,
- 15: true,
- } // type_5:true,type_7:true,type_23
- var type6 = {
- 1: true,
- }
- var 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.tokenTypes = {
- FUNCTION_WITH_ONE_ARG: 0,
- NUMBER: 1,
- BINARY_OPERATOR_HIGH_PRECENDENCE: 2,
- CONSTANT: 3,
- OPENING_PARENTHESIS: 4,
- CLOSING_PARENTHESIS: 5,
- DECIMAL: 6,
- POSTFIX_FUNCTION_WITH_ONE_ARG: 7,
- FUNCTION_WITH_N_ARGS: 8,
- BINARY_OPERATOR_LOW_PRECENDENCE: 9,
- BINARY_OPERATOR_PERMUTATION: 10,
- COMMA: 11,
- EVALUATED_FUNCTION: 12,
- EVALUATED_FUNCTION_PARAMETER: 13,
- SPACE: 14,
- }
- /**
-
- 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 and third parameter is a string that will be mexp string
- 13: variable of Sigma function
- */
- Mexp.addToken = function (newTokens) {
- for (var i = 0; i < newTokens.length; i++) {
- var x = newTokens[i].token.length
- var temp = -1
- if (newTokens[i].type === Mexp.tokenTypes.FUNCTION_WITH_N_ARGS && newTokens[i].numberOfArguments === undefined) {
- newTokens[i].numberOfArguments = 2
- }
- // newAr is a specially designed data structure index of 1d array = length of tokens
- newAr[x] = newAr[x] || []
- for (var y = 0; y < newAr[x].length; y++) {
- if (newTokens[i].token === newAr[x][y]) {
- temp = indexOfToken(newAr[x][y], tokens)
- break
- }
- }
- if (temp === -1) {
- tokens.push(newTokens[i])
- newTokens[i].precedence = preced[newTokens[i].type]
- if (newAr.length <= newTokens[i].token.length) {
- newAr[newTokens[i].token.length] = []
- }
- newAr[newTokens[i].token.length].push(newTokens[i].token)
- } else {
- // overwrite
- tokens[temp] = newTokens[i]
- newTokens[i].precedence = preced[newTokens[i].type]
- }
- }
- }
- function indexOfToken(key, tokens) {
- for (var search = 0; search < tokens.length; search++) {
- if (tokens[search].token === key) return search
- }
- return -1
- }
- function tokenize(string) {
- var nodes = []
- var length = string.length
- var key, x, y
- for (var i = 0; i < length; i++) {
- if (i < length - 1 && string[i] === ' ' && string[i + 1] === ' ') {
- continue
- }
- key = ''
- for (x = string.length - i > newAr.length - 2 ? newAr.length - 1 : string.length - i; x > 0; x--) {
- if (newAr[x] === undefined) continue
- for (y = 0; y < newAr[x].length; y++) {
- if (match(string, newAr[x][y], i, x)) {
- key = newAr[x][y]
- y = newAr[x].length
- x = 0
- }
- }
- }
- i += key.length - 1
- if (key === '') {
- throw new Mexp.Exception("Can't understand after " + string.slice(i))
- }
- nodes.push(tokens[indexOfToken(key, tokens)])
- }
- return nodes
- }
- var changeSignObj = {
- value: Mexp.math.changeSign,
- type: 0,
- pre: 21,
- show: '-',
- }
- var closingParObj = {
- value: ')',
- show: ')',
- type: 5,
- pre: 0,
- }
- var openingParObj = {
- value: '(',
- type: 4,
- pre: 0,
- show: '(',
- }
- Mexp.lex = function (inp, tokens) {
- 'use strict'
- var str = [openingParObj]
- var ptc = [] // Parenthesis to close at the beginning is after one token
- var inpStr = inp
- var allowed = type0
- var bracToClose = 0
- var asterick = empty
- var prevKey = ''
- var i
- if (typeof tokens !== 'undefined') {
- Mexp.addToken(tokens)
- }
- var obj = {}
- var nodes = tokenize(inpStr)
- for (i = 0; i < nodes.length; i++) {
- var node = nodes[i]
- if (node.type === 14) {
- if (
- i > 0 &&
- i < nodes.length - 1 &&
- nodes[i + 1].type === 1 &&
- (nodes[i - 1].type === 1 || nodes[i - 1].type === 6)
- ) {
- throw new Mexp.Exception('Unexpected Space')
- }
- continue
- }
- var cToken = node.token
- var cType = node.type
- var cEv = node.value
- var cPre = node.precedence
- var cShow = node.show
- var pre = str[str.length - 1]
- var j
- for (j = ptc.length; j--; ) {
- // loop over ptc
- if (ptc[j] === 0) {
- if ([0, 2, 3, 4, 5, 9, 11, 12, 13].indexOf(cType) !== -1) {
- if (allowed[cType] !== true) {
- throw new Mexp.Exception(cToken + ' is not allowed after ' + prevKey)
- }
- str.push(closingParObj)
- allowed = type1
- asterick = type3Asterick
- ptc.pop()
- }
- } else break
- }
- if (allowed[cType] !== true) {
- throw new Mexp.Exception(cToken + ' is not allowed after ' + prevKey)
- }
- if (asterick[cType] === true) {
- cType = 2
- cEv = Mexp.math.mul
- cShow = '×'
- cPre = 3
- i = i - 1
- }
- obj = {
- value: cEv,
- type: cType,
- pre: cPre,
- show: cShow,
- numberOfArguments: node.numberOfArguments,
- }
- if (cType === 0) {
- allowed = type0
- asterick = empty
- inc(ptc, 2)
- str.push(obj)
- if (nodes[i + 1].type !== 4) {
- str.push(openingParObj)
- ptc.push(2)
- }
- // bracToClose++
- } else if (cType === 1) {
- if (pre.type === 1) {
- pre.value += cEv
- inc(ptc, 1)
- } else {
- str.push(obj)
- }
- allowed = type1
- asterick = type1Asterick
- } 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 = type3Asterick
- } else if (cType === 4) {
- inc(ptc, 1)
- 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!!!')
- }
- bracToClose--
- allowed = type1
- asterick = type3Asterick
- str.push(obj)
- inc(ptc, 1)
- } 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 = type3Asterick
- inc(ptc, 1)
- str.push(obj)
- }
- if (cType === 8) {
- allowed = type0
- asterick = empty
- inc(ptc, node.numberOfArguments + 2)
- str.push(obj)
- // str.push(openingParObj)
- if (nodes[i + 1].type !== 4) {
- str.push(openingParObj)
- ptc.push(node.numberOfArguments + 2)
- }
- } 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(changeSignObj)
- str.push(openingParObj)
- }
- } 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)
- str.push(obj)
- if (nodes[i + 1].type !== 4) {
- str.push(openingParObj)
- ptc.push(6)
- }
- } else if (cType === 13) {
- allowed = type1
- asterick = type3Asterick
- str.push(obj)
- }
- inc(ptc, -1)
- prevKey = cToken
- }
- for (j = ptc.length; j--; ) {
- // loop over ptc
- str.push(closingParObj)
- }
- if (allowed[5] !== true) {
- throw new Mexp.Exception('complete the expression')
- }
- while (bracToClose--) {
- str.push(closingParObj)
- }
- str.push(closingParObj)
- // console.log(str);
- return new Mexp(str)
- }
- module.exports = Mexp
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