simple-squiggle

parse.js (48357B)

---

 import _extends from "@babel/runtime/helpers/extends";
 import { factory } from '../utils/factory.js';
 import { isAccessorNode, isConstantNode, isFunctionNode, isOperatorNode, isSymbolNode } from '../utils/is.js';
 import { deepMap } from '../utils/collection.js';
 import { hasOwnProperty } from '../utils/object.js';
 var name = 'parse';
 var dependencies = ['typed', 'numeric', 'config', 'AccessorNode', 'ArrayNode', 'AssignmentNode', 'BlockNode', 'ConditionalNode', 'ConstantNode', 'FunctionAssignmentNode', 'FunctionNode', 'IndexNode', 'ObjectNode', 'OperatorNode', 'ParenthesisNode', 'RangeNode', 'RelationalNode', 'SymbolNode'];
 export var createParse = /* #__PURE__ */factory(name, dependencies, _ref => {
   var {
     typed,
     numeric,
     config,
     AccessorNode,
     ArrayNode,
     AssignmentNode,
     BlockNode,
     ConditionalNode,
     ConstantNode,
     FunctionAssignmentNode,
     FunctionNode,
     IndexNode,
     ObjectNode,
     OperatorNode,
     ParenthesisNode,
     RangeNode,
     RelationalNode,
     SymbolNode
   } = _ref;
 
   /**
    * Parse an expression. Returns a node tree, which can be evaluated by
    * invoking node.evaluate().
    *
    * Note the evaluating arbitrary expressions may involve security risks,
    * see [https://mathjs.org/docs/expressions/security.html](https://mathjs.org/docs/expressions/security.html) for more information.
    *
    * Syntax:
    *
    *     math.parse(expr)
    *     math.parse(expr, options)
    *     math.parse([expr1, expr2, expr3, ...])
    *     math.parse([expr1, expr2, expr3, ...], options)
    *
    * Example:
    *
    *     const node1 = math.parse('sqrt(3^2 + 4^2)')
    *     node1.compile().evaluate() // 5
    *
    *     let scope = {a:3, b:4}
    *     const node2 = math.parse('a * b') // 12
    *     const code2 = node2.compile()
    *     code2.evaluate(scope) // 12
    *     scope.a = 5
    *     code2.evaluate(scope) // 20
    *
    *     const nodes = math.parse(['a = 3', 'b = 4', 'a * b'])
    *     nodes[2].compile().evaluate() // 12
    *
    * See also:
    *
    *     evaluate, compile
    *
    * @param {string | string[] | Matrix} expr          Expression to be parsed
    * @param {{nodes: Object<string, Node>}} [options]  Available options:
    *                                                   - `nodes` a set of custom nodes
    * @return {Node | Node[]} node
    * @throws {Error}
    */
   var parse = typed(name, {
     string: function string(expression) {
       return parseStart(expression, {});
     },
     'Array | Matrix': function ArrayMatrix(expressions) {
       return parseMultiple(expressions, {});
     },
     'string, Object': function stringObject(expression, options) {
       var extraNodes = options.nodes !== undefined ? options.nodes : {};
       return parseStart(expression, extraNodes);
     },
     'Array | Matrix, Object': parseMultiple
   });
 
   function parseMultiple(expressions) {
     var options = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {};
     var extraNodes = options.nodes !== undefined ? options.nodes : {}; // parse an array or matrix with expressions
 
     return deepMap(expressions, function (elem) {
       if (typeof elem !== 'string') throw new TypeError('String expected');
       return parseStart(elem, extraNodes);
     });
   } // token types enumeration
 
 
   var TOKENTYPE = {
     NULL: 0,
     DELIMITER: 1,
     NUMBER: 2,
     SYMBOL: 3,
     UNKNOWN: 4
   }; // map with all delimiters
 
   var DELIMITERS = {
     ',': true,
     '(': true,
     ')': true,
     '[': true,
     ']': true,
     '{': true,
     '}': true,
     '"': true,
     '\'': true,
     ';': true,
     '+': true,
     '-': true,
     '*': true,
     '.*': true,
     '/': true,
     './': true,
     '%': true,
     '^': true,
     '.^': true,
     '~': true,
     '!': true,
     '&': true,
     '|': true,
     '^|': true,
     '=': true,
     ':': true,
     '?': true,
     '==': true,
     '!=': true,
     '<': true,
     '>': true,
     '<=': true,
     '>=': true,
     '<<': true,
     '>>': true,
     '>>>': true
   }; // map with all named delimiters
 
   var NAMED_DELIMITERS = {
     mod: true,
     to: true,
     in: true,
     and: true,
     xor: true,
     or: true,
     not: true
   };
   var CONSTANTS = {
     true: true,
     false: false,
     null: null,
     undefined: undefined
   };
   var NUMERIC_CONSTANTS = ['NaN', 'Infinity'];
 
   function initialState() {
     return {
       extraNodes: {},
       // current extra nodes, must be careful not to mutate
       expression: '',
       // current expression
       comment: '',
       // last parsed comment
       index: 0,
       // current index in expr
       token: '',
       // current token
       tokenType: TOKENTYPE.NULL,
       // type of the token
       nestingLevel: 0,
       // level of nesting inside parameters, used to ignore newline characters
       conditionalLevel: null // when a conditional is being parsed, the level of the conditional is stored here
 
     };
   }
   /**
    * View upto `length` characters of the expression starting at the current character.
    *
    * @param {Object} state
    * @param {number} [length=1] Number of characters to view
    * @returns {string}
    * @private
    */
 
 
   function currentString(state, length) {
     return state.expression.substr(state.index, length);
   }
   /**
    * View the current character. Returns '' if end of expression is reached.
    *
    * @param {Object} state
    * @returns {string}
    * @private
    */
 
 
   function currentCharacter(state) {
     return currentString(state, 1);
   }
   /**
    * Get the next character from the expression.
    * The character is stored into the char c. If the end of the expression is
    * reached, the function puts an empty string in c.
    * @private
    */
 
 
   function next(state) {
     state.index++;
   }
   /**
    * Preview the previous character from the expression.
    * @return {string} cNext
    * @private
    */
 
 
   function prevCharacter(state) {
     return state.expression.charAt(state.index - 1);
   }
   /**
    * Preview the next character from the expression.
    * @return {string} cNext
    * @private
    */
 
 
   function nextCharacter(state) {
     return state.expression.charAt(state.index + 1);
   }
   /**
    * Get next token in the current string expr.
    * The token and token type are available as token and tokenType
    * @private
    */
 
 
   function getToken(state) {
     state.tokenType = TOKENTYPE.NULL;
     state.token = '';
     state.comment = ''; // skip over ignored characters:
 
     while (true) {
       // comments:
       if (currentCharacter(state) === '#') {
         while (currentCharacter(state) !== '\n' && currentCharacter(state) !== '') {
           state.comment += currentCharacter(state);
           next(state);
         }
       } // whitespace: space, tab, and newline when inside parameters
 
 
       if (parse.isWhitespace(currentCharacter(state), state.nestingLevel)) {
         next(state);
       } else {
         break;
       }
     } // check for end of expression
 
 
     if (currentCharacter(state) === '') {
       // token is still empty
       state.tokenType = TOKENTYPE.DELIMITER;
       return;
     } // check for new line character
 
 
     if (currentCharacter(state) === '\n' && !state.nestingLevel) {
       state.tokenType = TOKENTYPE.DELIMITER;
       state.token = currentCharacter(state);
       next(state);
       return;
     }
 
     var c1 = currentCharacter(state);
     var c2 = currentString(state, 2);
     var c3 = currentString(state, 3);
 
     if (c3.length === 3 && DELIMITERS[c3]) {
       state.tokenType = TOKENTYPE.DELIMITER;
       state.token = c3;
       next(state);
       next(state);
       next(state);
       return;
     } // check for delimiters consisting of 2 characters
 
 
     if (c2.length === 2 && DELIMITERS[c2]) {
       state.tokenType = TOKENTYPE.DELIMITER;
       state.token = c2;
       next(state);
       next(state);
       return;
     } // check for delimiters consisting of 1 character
 
 
     if (DELIMITERS[c1]) {
       state.tokenType = TOKENTYPE.DELIMITER;
       state.token = c1;
       next(state);
       return;
     } // check for a number
 
 
     if (parse.isDigitDot(c1)) {
       state.tokenType = TOKENTYPE.NUMBER; // check for binary, octal, or hex
 
       var _c = currentString(state, 2);
 
       if (_c === '0b' || _c === '0o' || _c === '0x') {
         state.token += currentCharacter(state);
         next(state);
         state.token += currentCharacter(state);
         next(state);
 
         while (parse.isHexDigit(currentCharacter(state))) {
           state.token += currentCharacter(state);
           next(state);
         }
 
         if (currentCharacter(state) === '.') {
           // this number has a radix point
           state.token += '.';
           next(state); // get the digits after the radix
 
           while (parse.isHexDigit(currentCharacter(state))) {
             state.token += currentCharacter(state);
             next(state);
           }
         } else if (currentCharacter(state) === 'i') {
           // this number has a word size suffix
           state.token += 'i';
           next(state); // get the word size
 
           while (parse.isDigit(currentCharacter(state))) {
             state.token += currentCharacter(state);
             next(state);
           }
         }
 
         return;
       } // get number, can have a single dot
 
 
       if (currentCharacter(state) === '.') {
         state.token += currentCharacter(state);
         next(state);
 
         if (!parse.isDigit(currentCharacter(state))) {
           // this is no number, it is just a dot (can be dot notation)
           state.tokenType = TOKENTYPE.DELIMITER;
           return;
         }
       } else {
         while (parse.isDigit(currentCharacter(state))) {
           state.token += currentCharacter(state);
           next(state);
         }
 
         if (parse.isDecimalMark(currentCharacter(state), nextCharacter(state))) {
           state.token += currentCharacter(state);
           next(state);
         }
       }
 
       while (parse.isDigit(currentCharacter(state))) {
         state.token += currentCharacter(state);
         next(state);
       } // check for exponential notation like "2.3e-4", "1.23e50" or "2e+4"
 
 
       if (currentCharacter(state) === 'E' || currentCharacter(state) === 'e') {
         if (parse.isDigit(nextCharacter(state)) || nextCharacter(state) === '-' || nextCharacter(state) === '+') {
           state.token += currentCharacter(state);
           next(state);
 
           if (currentCharacter(state) === '+' || currentCharacter(state) === '-') {
             state.token += currentCharacter(state);
             next(state);
           } // Scientific notation MUST be followed by an exponent
 
 
           if (!parse.isDigit(currentCharacter(state))) {
             throw createSyntaxError(state, 'Digit expected, got "' + currentCharacter(state) + '"');
           }
 
           while (parse.isDigit(currentCharacter(state))) {
             state.token += currentCharacter(state);
             next(state);
           }
 
           if (parse.isDecimalMark(currentCharacter(state), nextCharacter(state))) {
             throw createSyntaxError(state, 'Digit expected, got "' + currentCharacter(state) + '"');
           }
         } else if (nextCharacter(state) === '.') {
           next(state);
           throw createSyntaxError(state, 'Digit expected, got "' + currentCharacter(state) + '"');
         }
       }
 
       return;
     } // check for variables, functions, named operators
 
 
     if (parse.isAlpha(currentCharacter(state), prevCharacter(state), nextCharacter(state))) {
       while (parse.isAlpha(currentCharacter(state), prevCharacter(state), nextCharacter(state)) || parse.isDigit(currentCharacter(state))) {
         state.token += currentCharacter(state);
         next(state);
       }
 
       if (hasOwnProperty(NAMED_DELIMITERS, state.token)) {
         state.tokenType = TOKENTYPE.DELIMITER;
       } else {
         state.tokenType = TOKENTYPE.SYMBOL;
       }
 
       return;
     } // something unknown is found, wrong characters -> a syntax error
 
 
     state.tokenType = TOKENTYPE.UNKNOWN;
 
     while (currentCharacter(state) !== '') {
       state.token += currentCharacter(state);
       next(state);
     }
 
     throw createSyntaxError(state, 'Syntax error in part "' + state.token + '"');
   }
   /**
    * Get next token and skip newline tokens
    */
 
 
   function getTokenSkipNewline(state) {
     do {
       getToken(state);
     } while (state.token === '\n'); // eslint-disable-line no-unmodified-loop-condition
 
   }
   /**
    * Open parameters.
    * New line characters will be ignored until closeParams(state) is called
    */
 
 
   function openParams(state) {
     state.nestingLevel++;
   }
   /**
    * Close parameters.
    * New line characters will no longer be ignored
    */
 
 
   function closeParams(state) {
     state.nestingLevel--;
   }
   /**
    * Checks whether the current character `c` is a valid alpha character:
    *
    * - A latin letter (upper or lower case) Ascii: a-z, A-Z
    * - An underscore                        Ascii: _
    * - A dollar sign                        Ascii: $
    * - A latin letter with accents          Unicode: \u00C0 - \u02AF
    * - A greek letter                       Unicode: \u0370 - \u03FF
    * - A mathematical alphanumeric symbol   Unicode: \u{1D400} - \u{1D7FF} excluding invalid code points
    *
    * The previous and next characters are needed to determine whether
    * this character is part of a unicode surrogate pair.
    *
    * @param {string} c      Current character in the expression
    * @param {string} cPrev  Previous character
    * @param {string} cNext  Next character
    * @return {boolean}
    */
 
 
   parse.isAlpha = function isAlpha(c, cPrev, cNext) {
     return parse.isValidLatinOrGreek(c) || parse.isValidMathSymbol(c, cNext) || parse.isValidMathSymbol(cPrev, c);
   };
   /**
    * Test whether a character is a valid latin, greek, or letter-like character
    * @param {string} c
    * @return {boolean}
    */
 
 
   parse.isValidLatinOrGreek = function isValidLatinOrGreek(c) {
     return /^[a-zA-Z_$\u00C0-\u02AF\u0370-\u03FF\u2100-\u214F]$/.test(c);
   };
   /**
    * Test whether two given 16 bit characters form a surrogate pair of a
    * unicode math symbol.
    *
    * https://unicode-table.com/en/
    * https://www.wikiwand.com/en/Mathematical_operators_and_symbols_in_Unicode
    *
    * Note: In ES6 will be unicode aware:
    * https://stackoverflow.com/questions/280712/javascript-unicode-regexes
    * https://mathiasbynens.be/notes/es6-unicode-regex
    *
    * @param {string} high
    * @param {string} low
    * @return {boolean}
    */
 
 
   parse.isValidMathSymbol = function isValidMathSymbol(high, low) {
     return /^[\uD835]$/.test(high) && /^[\uDC00-\uDFFF]$/.test(low) && /^[^\uDC55\uDC9D\uDCA0\uDCA1\uDCA3\uDCA4\uDCA7\uDCA8\uDCAD\uDCBA\uDCBC\uDCC4\uDD06\uDD0B\uDD0C\uDD15\uDD1D\uDD3A\uDD3F\uDD45\uDD47-\uDD49\uDD51\uDEA6\uDEA7\uDFCC\uDFCD]$/.test(low);
   };
   /**
    * Check whether given character c is a white space character: space, tab, or enter
    * @param {string} c
    * @param {number} nestingLevel
    * @return {boolean}
    */
 
 
   parse.isWhitespace = function isWhitespace(c, nestingLevel) {
     // TODO: also take '\r' carriage return as newline? Or does that give problems on mac?
     return c === ' ' || c === '\t' || c === '\n' && nestingLevel > 0;
   };
   /**
    * Test whether the character c is a decimal mark (dot).
    * This is the case when it's not the start of a delimiter '.*', './', or '.^'
    * @param {string} c
    * @param {string} cNext
    * @return {boolean}
    */
 
 
   parse.isDecimalMark = function isDecimalMark(c, cNext) {
     return c === '.' && cNext !== '/' && cNext !== '*' && cNext !== '^';
   };
   /**
    * checks if the given char c is a digit or dot
    * @param {string} c   a string with one character
    * @return {boolean}
    */
 
 
   parse.isDigitDot = function isDigitDot(c) {
     return c >= '0' && c <= '9' || c === '.';
   };
   /**
    * checks if the given char c is a digit
    * @param {string} c   a string with one character
    * @return {boolean}
    */
 
 
   parse.isDigit = function isDigit(c) {
     return c >= '0' && c <= '9';
   };
   /**
    * checks if the given char c is a hex digit
    * @param {string} c   a string with one character
    * @return {boolean}
    */
 
 
   parse.isHexDigit = function isHexDigit(c) {
     return c >= '0' && c <= '9' || c >= 'a' && c <= 'f' || c >= 'A' && c <= 'F';
   };
   /**
    * Start of the parse levels below, in order of precedence
    * @return {Node} node
    * @private
    */
 
 
   function parseStart(expression, extraNodes) {
     var state = initialState();
 
     _extends(state, {
       expression,
       extraNodes
     });
 
     getToken(state);
     var node = parseBlock(state); // check for garbage at the end of the expression
     // an expression ends with a empty character '' and tokenType DELIMITER
 
     if (state.token !== '') {
       if (state.tokenType === TOKENTYPE.DELIMITER) {
         // user entered a not existing operator like "//"
         // TODO: give hints for aliases, for example with "<>" give as hint " did you mean !== ?"
         throw createError(state, 'Unexpected operator ' + state.token);
       } else {
         throw createSyntaxError(state, 'Unexpected part "' + state.token + '"');
       }
     }
 
     return node;
   }
   /**
    * Parse a block with expressions. Expressions can be separated by a newline
    * character '\n', or by a semicolon ';'. In case of a semicolon, no output
    * of the preceding line is returned.
    * @return {Node} node
    * @private
    */
 
 
   function parseBlock(state) {
     var node;
     var blocks = [];
     var visible;
 
     if (state.token !== '' && state.token !== '\n' && state.token !== ';') {
       node = parseAssignment(state);
       node.comment = state.comment;
     } // TODO: simplify this loop
 
 
     while (state.token === '\n' || state.token === ';') {
       // eslint-disable-line no-unmodified-loop-condition
       if (blocks.length === 0 && node) {
         visible = state.token !== ';';
         blocks.push({
           node: node,
           visible: visible
         });
       }
 
       getToken(state);
 
       if (state.token !== '\n' && state.token !== ';' && state.token !== '') {
         node = parseAssignment(state);
         node.comment = state.comment;
         visible = state.token !== ';';
         blocks.push({
           node: node,
           visible: visible
         });
       }
     }
 
     if (blocks.length > 0) {
       return new BlockNode(blocks);
     } else {
       if (!node) {
         node = new ConstantNode(undefined);
         node.comment = state.comment;
       }
 
       return node;
     }
   }
   /**
    * Assignment of a function or variable,
    * - can be a variable like 'a=2.3'
    * - or a updating an existing variable like 'matrix(2,3:5)=[6,7,8]'
    * - defining a function like 'f(x) = x^2'
    * @return {Node} node
    * @private
    */
 
 
   function parseAssignment(state) {
     var name, args, value, valid;
     var node = parseConditional(state);
 
     if (state.token === '=') {
       if (isSymbolNode(node)) {
         // parse a variable assignment like 'a = 2/3'
         name = node.name;
         getTokenSkipNewline(state);
         value = parseAssignment(state);
         return new AssignmentNode(new SymbolNode(name), value);
       } else if (isAccessorNode(node)) {
         // parse a matrix subset assignment like 'A[1,2] = 4'
         getTokenSkipNewline(state);
         value = parseAssignment(state);
         return new AssignmentNode(node.object, node.index, value);
       } else if (isFunctionNode(node) && isSymbolNode(node.fn)) {
         // parse function assignment like 'f(x) = x^2'
         valid = true;
         args = [];
         name = node.name;
         node.args.forEach(function (arg, index) {
           if (isSymbolNode(arg)) {
             args[index] = arg.name;
           } else {
             valid = false;
           }
         });
 
         if (valid) {
           getTokenSkipNewline(state);
           value = parseAssignment(state);
           return new FunctionAssignmentNode(name, args, value);
         }
       }
 
       throw createSyntaxError(state, 'Invalid left hand side of assignment operator =');
     }
 
     return node;
   }
   /**
    * conditional operation
    *
    *     condition ? truePart : falsePart
    *
    * Note: conditional operator is right-associative
    *
    * @return {Node} node
    * @private
    */
 
 
   function parseConditional(state) {
     var node = parseLogicalOr(state);
 
     while (state.token === '?') {
       // eslint-disable-line no-unmodified-loop-condition
       // set a conditional level, the range operator will be ignored as long
       // as conditionalLevel === state.nestingLevel.
       var prev = state.conditionalLevel;
       state.conditionalLevel = state.nestingLevel;
       getTokenSkipNewline(state);
       var condition = node;
       var trueExpr = parseAssignment(state);
       if (state.token !== ':') throw createSyntaxError(state, 'False part of conditional expression expected');
       state.conditionalLevel = null;
       getTokenSkipNewline(state);
       var falseExpr = parseAssignment(state); // Note: check for conditional operator again, right associativity
 
       node = new ConditionalNode(condition, trueExpr, falseExpr); // restore the previous conditional level
 
       state.conditionalLevel = prev;
     }
 
     return node;
   }
   /**
    * logical or, 'x or y'
    * @return {Node} node
    * @private
    */
 
 
   function parseLogicalOr(state) {
     var node = parseLogicalXor(state);
 
     while (state.token === 'or') {
       // eslint-disable-line no-unmodified-loop-condition
       getTokenSkipNewline(state);
       node = new OperatorNode('or', 'or', [node, parseLogicalXor(state)]);
     }
 
     return node;
   }
   /**
    * logical exclusive or, 'x xor y'
    * @return {Node} node
    * @private
    */
 
 
   function parseLogicalXor(state) {
     var node = parseLogicalAnd(state);
 
     while (state.token === 'xor') {
       // eslint-disable-line no-unmodified-loop-condition
       getTokenSkipNewline(state);
       node = new OperatorNode('xor', 'xor', [node, parseLogicalAnd(state)]);
     }
 
     return node;
   }
   /**
    * logical and, 'x and y'
    * @return {Node} node
    * @private
    */
 
 
   function parseLogicalAnd(state) {
     var node = parseBitwiseOr(state);
 
     while (state.token === 'and') {
       // eslint-disable-line no-unmodified-loop-condition
       getTokenSkipNewline(state);
       node = new OperatorNode('and', 'and', [node, parseBitwiseOr(state)]);
     }
 
     return node;
   }
   /**
    * bitwise or, 'x | y'
    * @return {Node} node
    * @private
    */
 
 
   function parseBitwiseOr(state) {
     var node = parseBitwiseXor(state);
 
     while (state.token === '|') {
       // eslint-disable-line no-unmodified-loop-condition
       getTokenSkipNewline(state);
       node = new OperatorNode('|', 'bitOr', [node, parseBitwiseXor(state)]);
     }
 
     return node;
   }
   /**
    * bitwise exclusive or (xor), 'x ^| y'
    * @return {Node} node
    * @private
    */
 
 
   function parseBitwiseXor(state) {
     var node = parseBitwiseAnd(state);
 
     while (state.token === '^|') {
       // eslint-disable-line no-unmodified-loop-condition
       getTokenSkipNewline(state);
       node = new OperatorNode('^|', 'bitXor', [node, parseBitwiseAnd(state)]);
     }
 
     return node;
   }
   /**
    * bitwise and, 'x & y'
    * @return {Node} node
    * @private
    */
 
 
   function parseBitwiseAnd(state) {
     var node = parseRelational(state);
 
     while (state.token === '&') {
       // eslint-disable-line no-unmodified-loop-condition
       getTokenSkipNewline(state);
       node = new OperatorNode('&', 'bitAnd', [node, parseRelational(state)]);
     }
 
     return node;
   }
   /**
    * Parse a chained conditional, like 'a > b >= c'
    * @return {Node} node
    */
 
 
   function parseRelational(state) {
     var params = [parseShift(state)];
     var conditionals = [];
     var operators = {
       '==': 'equal',
       '!=': 'unequal',
       '<': 'smaller',
       '>': 'larger',
       '<=': 'smallerEq',
       '>=': 'largerEq'
     };
 
     while (hasOwnProperty(operators, state.token)) {
       // eslint-disable-line no-unmodified-loop-condition
       var cond = {
         name: state.token,
         fn: operators[state.token]
       };
       conditionals.push(cond);
       getTokenSkipNewline(state);
       params.push(parseShift(state));
     }
 
     if (params.length === 1) {
       return params[0];
     } else if (params.length === 2) {
       return new OperatorNode(conditionals[0].name, conditionals[0].fn, params);
     } else {
       return new RelationalNode(conditionals.map(c => c.fn), params);
     }
   }
   /**
    * Bitwise left shift, bitwise right arithmetic shift, bitwise right logical shift
    * @return {Node} node
    * @private
    */
 
 
   function parseShift(state) {
     var node, name, fn, params;
     node = parseConversion(state);
     var operators = {
       '<<': 'leftShift',
       '>>': 'rightArithShift',
       '>>>': 'rightLogShift'
     };
 
     while (hasOwnProperty(operators, state.token)) {
       name = state.token;
       fn = operators[name];
       getTokenSkipNewline(state);
       params = [node, parseConversion(state)];
       node = new OperatorNode(name, fn, params);
     }
 
     return node;
   }
   /**
    * conversion operators 'to' and 'in'
    * @return {Node} node
    * @private
    */
 
 
   function parseConversion(state) {
     var node, name, fn, params;
     node = parseRange(state);
     var operators = {
       to: 'to',
       in: 'to' // alias of 'to'
 
     };
 
     while (hasOwnProperty(operators, state.token)) {
       name = state.token;
       fn = operators[name];
       getTokenSkipNewline(state);
 
       if (name === 'in' && state.token === '') {
         // end of expression -> this is the unit 'in' ('inch')
         node = new OperatorNode('*', 'multiply', [node, new SymbolNode('in')], true);
       } else {
         // operator 'a to b' or 'a in b'
         params = [node, parseRange(state)];
         node = new OperatorNode(name, fn, params);
       }
     }
 
     return node;
   }
   /**
    * parse range, "start:end", "start:step:end", ":", "start:", ":end", etc
    * @return {Node} node
    * @private
    */
 
 
   function parseRange(state) {
     var node;
     var params = [];
 
     if (state.token === ':') {
       // implicit start=1 (one-based)
       node = new ConstantNode(1);
     } else {
       // explicit start
       node = parseAddSubtract(state);
     }
 
     if (state.token === ':' && state.conditionalLevel !== state.nestingLevel) {
       // we ignore the range operator when a conditional operator is being processed on the same level
       params.push(node); // parse step and end
 
       while (state.token === ':' && params.length < 3) {
         // eslint-disable-line no-unmodified-loop-condition
         getTokenSkipNewline(state);
 
         if (state.token === ')' || state.token === ']' || state.token === ',' || state.token === '') {
           // implicit end
           params.push(new SymbolNode('end'));
         } else {
           // explicit end
           params.push(parseAddSubtract(state));
         }
       }
 
       if (params.length === 3) {
         // params = [start, step, end]
         node = new RangeNode(params[0], params[2], params[1]); // start, end, step
       } else {
         // length === 2
         // params = [start, end]
         node = new RangeNode(params[0], params[1]); // start, end
       }
     }
 
     return node;
   }
   /**
    * add or subtract
    * @return {Node} node
    * @private
    */
 
 
   function parseAddSubtract(state) {
     var node, name, fn, params;
     node = parseMultiplyDivide(state);
     var operators = {
       '+': 'add',
       '-': 'subtract'
     };
 
     while (hasOwnProperty(operators, state.token)) {
       name = state.token;
       fn = operators[name];
       getTokenSkipNewline(state);
       var rightNode = parseMultiplyDivide(state);
 
       if (rightNode.isPercentage) {
         params = [node, new OperatorNode('*', 'multiply', [node, rightNode])];
       } else {
         params = [node, rightNode];
       }
 
       node = new OperatorNode(name, fn, params);
     }
 
     return node;
   }
   /**
    * multiply, divide, modulus
    * @return {Node} node
    * @private
    */
 
 
   function parseMultiplyDivide(state) {
     var node, last, name, fn;
     node = parseImplicitMultiplication(state);
     last = node;
     var operators = {
       '*': 'multiply',
       '.*': 'dotMultiply',
       '/': 'divide',
       './': 'dotDivide'
     };
 
     while (true) {
       if (hasOwnProperty(operators, state.token)) {
         // explicit operators
         name = state.token;
         fn = operators[name];
         getTokenSkipNewline(state);
         last = parseImplicitMultiplication(state);
         node = new OperatorNode(name, fn, [node, last]);
       } else {
         break;
       }
     }
 
     return node;
   }
   /**
    * implicit multiplication
    * @return {Node} node
    * @private
    */
 
 
   function parseImplicitMultiplication(state) {
     var node, last;
     node = parseRule2(state);
     last = node;
 
     while (true) {
       if (state.tokenType === TOKENTYPE.SYMBOL || state.token === 'in' && isConstantNode(node) || state.tokenType === TOKENTYPE.NUMBER && !isConstantNode(last) && (!isOperatorNode(last) || last.op === '!') || state.token === '(') {
         // parse implicit multiplication
         //
         // symbol:      implicit multiplication like '2a', '(2+3)a', 'a b'
         // number:      implicit multiplication like '(2+3)2'
         // parenthesis: implicit multiplication like '2(3+4)', '(3+4)(1+2)'
         last = parseRule2(state);
         node = new OperatorNode('*', 'multiply', [node, last], true
         /* implicit */
         );
       } else {
         break;
       }
     }
 
     return node;
   }
   /**
    * Infamous "rule 2" as described in https://github.com/josdejong/mathjs/issues/792#issuecomment-361065370
    * Explicit division gets higher precedence than implicit multiplication
    * when the division matches this pattern: [number] / [number] [symbol]
    * @return {Node} node
    * @private
    */
 
 
   function parseRule2(state) {
     var node = parsePercentage(state);
     var last = node;
     var tokenStates = [];
 
     while (true) {
       // Match the "number /" part of the pattern "number / number symbol"
       if (state.token === '/' && isConstantNode(last)) {
         // Look ahead to see if the next token is a number
         tokenStates.push(_extends({}, state));
         getTokenSkipNewline(state); // Match the "number / number" part of the pattern
 
         if (state.tokenType === TOKENTYPE.NUMBER) {
           // Look ahead again
           tokenStates.push(_extends({}, state));
           getTokenSkipNewline(state); // Match the "symbol" part of the pattern, or a left parenthesis
 
           if (state.tokenType === TOKENTYPE.SYMBOL || state.token === '(') {
             // We've matched the pattern "number / number symbol".
             // Rewind once and build the "number / number" node; the symbol will be consumed later
             _extends(state, tokenStates.pop());
 
             tokenStates.pop();
             last = parsePercentage(state);
             node = new OperatorNode('/', 'divide', [node, last]);
           } else {
             // Not a match, so rewind
             tokenStates.pop();
 
             _extends(state, tokenStates.pop());
 
             break;
           }
         } else {
           // Not a match, so rewind
           _extends(state, tokenStates.pop());
 
           break;
         }
       } else {
         break;
       }
     }
 
     return node;
   }
   /**
    * percentage or mod
    * @return {Node} node
    * @private
    */
 
 
   function parsePercentage(state) {
     var node, name, fn, params;
     node = parseUnary(state);
     var operators = {
       '%': 'mod',
       mod: 'mod'
     };
 
     while (hasOwnProperty(operators, state.token)) {
       name = state.token;
       fn = operators[name];
       getTokenSkipNewline(state);
 
       if (name === '%' && state.tokenType === TOKENTYPE.DELIMITER && state.token !== '(') {
         // If the expression contains only %, then treat that as /100
         node = new OperatorNode('/', 'divide', [node, new ConstantNode(100)], false, true);
       } else {
         params = [node, parseUnary(state)];
         node = new OperatorNode(name, fn, params);
       }
     }
 
     return node;
   }
   /**
    * Unary plus and minus, and logical and bitwise not
    * @return {Node} node
    * @private
    */
 
 
   function parseUnary(state) {
     var name, params, fn;
     var operators = {
       '-': 'unaryMinus',
       '+': 'unaryPlus',
       '~': 'bitNot',
       not: 'not'
     };
 
     if (hasOwnProperty(operators, state.token)) {
       fn = operators[state.token];
       name = state.token;
       getTokenSkipNewline(state);
       params = [parseUnary(state)];
       return new OperatorNode(name, fn, params);
     }
 
     return parsePow(state);
   }
   /**
    * power
    * Note: power operator is right associative
    * @return {Node} node
    * @private
    */
 
 
   function parsePow(state) {
     var node, name, fn, params;
     node = parseLeftHandOperators(state);
 
     if (state.token === '^' || state.token === '.^') {
       name = state.token;
       fn = name === '^' ? 'pow' : 'dotPow';
       getTokenSkipNewline(state);
       params = [node, parseUnary(state)]; // Go back to unary, we can have '2^-3'
 
       node = new OperatorNode(name, fn, params);
     }
 
     return node;
   }
   /**
    * Left hand operators: factorial x!, ctranspose x'
    * @return {Node} node
    * @private
    */
 
 
   function parseLeftHandOperators(state) {
     var node, name, fn, params;
     node = parseCustomNodes(state);
     var operators = {
       '!': 'factorial',
       '\'': 'ctranspose'
     };
 
     while (hasOwnProperty(operators, state.token)) {
       name = state.token;
       fn = operators[name];
       getToken(state);
       params = [node];
       node = new OperatorNode(name, fn, params);
       node = parseAccessors(state, node);
     }
 
     return node;
   }
   /**
    * Parse a custom node handler. A node handler can be used to process
    * nodes in a custom way, for example for handling a plot.
    *
    * A handler must be passed as second argument of the parse function.
    * - must extend math.Node
    * - must contain a function _compile(defs: Object) : string
    * - must contain a function find(filter: Object) : Node[]
    * - must contain a function toString() : string
    * - the constructor is called with a single argument containing all parameters
    *
    * For example:
    *
    *     nodes = {
    *       'plot': PlotHandler
    *     }
    *
    * The constructor of the handler is called as:
    *
    *     node = new PlotHandler(params)
    *
    * The handler will be invoked when evaluating an expression like:
    *
    *     node = math.parse('plot(sin(x), x)', nodes)
    *
    * @return {Node} node
    * @private
    */
 
 
   function parseCustomNodes(state) {
     var params = [];
 
     if (state.tokenType === TOKENTYPE.SYMBOL && hasOwnProperty(state.extraNodes, state.token)) {
       var CustomNode = state.extraNodes[state.token];
       getToken(state); // parse parameters
 
       if (state.token === '(') {
         params = [];
         openParams(state);
         getToken(state);
 
         if (state.token !== ')') {
           params.push(parseAssignment(state)); // parse a list with parameters
 
           while (state.token === ',') {
             // eslint-disable-line no-unmodified-loop-condition
             getToken(state);
             params.push(parseAssignment(state));
           }
         }
 
         if (state.token !== ')') {
           throw createSyntaxError(state, 'Parenthesis ) expected');
         }
 
         closeParams(state);
         getToken(state);
       } // create a new custom node
       // noinspection JSValidateTypes
 
 
       return new CustomNode(params);
     }
 
     return parseSymbol(state);
   }
   /**
    * parse symbols: functions, variables, constants, units
    * @return {Node} node
    * @private
    */
 
 
   function parseSymbol(state) {
     var node, name;
 
     if (state.tokenType === TOKENTYPE.SYMBOL || state.tokenType === TOKENTYPE.DELIMITER && state.token in NAMED_DELIMITERS) {
       name = state.token;
       getToken(state);
 
       if (hasOwnProperty(CONSTANTS, name)) {
         // true, false, null, ...
         node = new ConstantNode(CONSTANTS[name]);
       } else if (NUMERIC_CONSTANTS.indexOf(name) !== -1) {
         // NaN, Infinity
         node = new ConstantNode(numeric(name, 'number'));
       } else {
         node = new SymbolNode(name);
       } // parse function parameters and matrix index
 
 
       node = parseAccessors(state, node);
       return node;
     }
 
     return parseDoubleQuotesString(state);
   }
   /**
    * parse accessors:
    * - function invocation in round brackets (...), for example sqrt(2)
    * - index enclosed in square brackets [...], for example A[2,3]
    * - dot notation for properties, like foo.bar
    * @param {Object} state
    * @param {Node} node    Node on which to apply the parameters. If there
    *                       are no parameters in the expression, the node
    *                       itself is returned
    * @param {string[]} [types]  Filter the types of notations
    *                            can be ['(', '[', '.']
    * @return {Node} node
    * @private
    */
 
 
   function parseAccessors(state, node, types) {
     var params;
 
     while ((state.token === '(' || state.token === '[' || state.token === '.') && (!types || types.indexOf(state.token) !== -1)) {
       // eslint-disable-line no-unmodified-loop-condition
       params = [];
 
       if (state.token === '(') {
         if (isSymbolNode(node) || isAccessorNode(node)) {
           // function invocation like fn(2, 3) or obj.fn(2, 3)
           openParams(state);
           getToken(state);
 
           if (state.token !== ')') {
             params.push(parseAssignment(state)); // parse a list with parameters
 
             while (state.token === ',') {
               // eslint-disable-line no-unmodified-loop-condition
               getToken(state);
               params.push(parseAssignment(state));
             }
           }
 
           if (state.token !== ')') {
             throw createSyntaxError(state, 'Parenthesis ) expected');
           }
 
           closeParams(state);
           getToken(state);
           node = new FunctionNode(node, params);
         } else {
           // implicit multiplication like (2+3)(4+5) or sqrt(2)(1+2)
           // don't parse it here but let it be handled by parseImplicitMultiplication
           // with correct precedence
           return node;
         }
       } else if (state.token === '[') {
         // index notation like variable[2, 3]
         openParams(state);
         getToken(state);
 
         if (state.token !== ']') {
           params.push(parseAssignment(state)); // parse a list with parameters
 
           while (state.token === ',') {
             // eslint-disable-line no-unmodified-loop-condition
             getToken(state);
             params.push(parseAssignment(state));
           }
         }
 
         if (state.token !== ']') {
           throw createSyntaxError(state, 'Parenthesis ] expected');
         }
 
         closeParams(state);
         getToken(state);
         node = new AccessorNode(node, new IndexNode(params));
       } else {
         // dot notation like variable.prop
         getToken(state);
 
         if (state.tokenType !== TOKENTYPE.SYMBOL) {
           throw createSyntaxError(state, 'Property name expected after dot');
         }
 
         params.push(new ConstantNode(state.token));
         getToken(state);
         var dotNotation = true;
         node = new AccessorNode(node, new IndexNode(params, dotNotation));
       }
     }
 
     return node;
   }
   /**
    * Parse a double quotes string.
    * @return {Node} node
    * @private
    */
 
 
   function parseDoubleQuotesString(state) {
     var node, str;
 
     if (state.token === '"') {
       str = parseDoubleQuotesStringToken(state); // create constant
 
       node = new ConstantNode(str); // parse index parameters
 
       node = parseAccessors(state, node);
       return node;
     }
 
     return parseSingleQuotesString(state);
   }
   /**
    * Parse a string surrounded by double quotes "..."
    * @return {string}
    */
 
 
   function parseDoubleQuotesStringToken(state) {
     var str = '';
 
     while (currentCharacter(state) !== '' && currentCharacter(state) !== '"') {
       if (currentCharacter(state) === '\\') {
         // escape character, immediately process the next
         // character to prevent stopping at a next '\"'
         str += currentCharacter(state);
         next(state);
       }
 
       str += currentCharacter(state);
       next(state);
     }
 
     getToken(state);
 
     if (state.token !== '"') {
       throw createSyntaxError(state, 'End of string " expected');
     }
 
     getToken(state);
     return JSON.parse('"' + str + '"'); // unescape escaped characters
   }
   /**
    * Parse a single quotes string.
    * @return {Node} node
    * @private
    */
 
 
   function parseSingleQuotesString(state) {
     var node, str;
 
     if (state.token === '\'') {
       str = parseSingleQuotesStringToken(state); // create constant
 
       node = new ConstantNode(str); // parse index parameters
 
       node = parseAccessors(state, node);
       return node;
     }
 
     return parseMatrix(state);
   }
   /**
    * Parse a string surrounded by single quotes '...'
    * @return {string}
    */
 
 
   function parseSingleQuotesStringToken(state) {
     var str = '';
 
     while (currentCharacter(state) !== '' && currentCharacter(state) !== '\'') {
       if (currentCharacter(state) === '\\') {
         // escape character, immediately process the next
         // character to prevent stopping at a next '\''
         str += currentCharacter(state);
         next(state);
       }
 
       str += currentCharacter(state);
       next(state);
     }
 
     getToken(state);
 
     if (state.token !== '\'') {
       throw createSyntaxError(state, 'End of string \' expected');
     }
 
     getToken(state);
     return JSON.parse('"' + str + '"'); // unescape escaped characters
   }
   /**
    * parse the matrix
    * @return {Node} node
    * @private
    */
 
 
   function parseMatrix(state) {
     var array, params, rows, cols;
 
     if (state.token === '[') {
       // matrix [...]
       openParams(state);
       getToken(state);
 
       if (state.token !== ']') {
         // this is a non-empty matrix
         var row = parseRow(state);
 
         if (state.token === ';') {
           // 2 dimensional array
           rows = 1;
           params = [row]; // the rows of the matrix are separated by dot-comma's
 
           while (state.token === ';') {
             // eslint-disable-line no-unmodified-loop-condition
             getToken(state);
             params[rows] = parseRow(state);
             rows++;
           }
 
           if (state.token !== ']') {
             throw createSyntaxError(state, 'End of matrix ] expected');
           }
 
           closeParams(state);
           getToken(state); // check if the number of columns matches in all rows
 
           cols = params[0].items.length;
 
           for (var r = 1; r < rows; r++) {
             if (params[r].items.length !== cols) {
               throw createError(state, 'Column dimensions mismatch ' + '(' + params[r].items.length + ' !== ' + cols + ')');
             }
           }
 
           array = new ArrayNode(params);
         } else {
           // 1 dimensional vector
           if (state.token !== ']') {
             throw createSyntaxError(state, 'End of matrix ] expected');
           }
 
           closeParams(state);
           getToken(state);
           array = row;
         }
       } else {
         // this is an empty matrix "[ ]"
         closeParams(state);
         getToken(state);
         array = new ArrayNode([]);
       }
 
       return parseAccessors(state, array);
     }
 
     return parseObject(state);
   }
   /**
    * Parse a single comma-separated row from a matrix, like 'a, b, c'
    * @return {ArrayNode} node
    */
 
 
   function parseRow(state) {
     var params = [parseAssignment(state)];
     var len = 1;
 
     while (state.token === ',') {
       // eslint-disable-line no-unmodified-loop-condition
       getToken(state); // parse expression
 
       params[len] = parseAssignment(state);
       len++;
     }
 
     return new ArrayNode(params);
   }
   /**
    * parse an object, enclosed in angle brackets{...}, for example {value: 2}
    * @return {Node} node
    * @private
    */
 
 
   function parseObject(state) {
     if (state.token === '{') {
       openParams(state);
       var key;
       var properties = {};
 
       do {
         getToken(state);
 
         if (state.token !== '}') {
           // parse key
           if (state.token === '"') {
             key = parseDoubleQuotesStringToken(state);
           } else if (state.token === '\'') {
             key = parseSingleQuotesStringToken(state);
           } else if (state.tokenType === TOKENTYPE.SYMBOL || state.tokenType === TOKENTYPE.DELIMITER && state.token in NAMED_DELIMITERS) {
             key = state.token;
             getToken(state);
           } else {
             throw createSyntaxError(state, 'Symbol or string expected as object key');
           } // parse key/value separator
 
 
           if (state.token !== ':') {
             throw createSyntaxError(state, 'Colon : expected after object key');
           }
 
           getToken(state); // parse key
 
           properties[key] = parseAssignment(state);
         }
       } while (state.token === ','); // eslint-disable-line no-unmodified-loop-condition
 
 
       if (state.token !== '}') {
         throw createSyntaxError(state, 'Comma , or bracket } expected after object value');
       }
 
       closeParams(state);
       getToken(state);
       var node = new ObjectNode(properties); // parse index parameters
 
       node = parseAccessors(state, node);
       return node;
     }
 
     return parseNumber(state);
   }
   /**
    * parse a number
    * @return {Node} node
    * @private
    */
 
 
   function parseNumber(state) {
     var numberStr;
 
     if (state.tokenType === TOKENTYPE.NUMBER) {
       // this is a number
       numberStr = state.token;
       getToken(state);
       return new ConstantNode(numeric(numberStr, config.number));
     }
 
     return parseParentheses(state);
   }
   /**
    * parentheses
    * @return {Node} node
    * @private
    */
 
 
   function parseParentheses(state) {
     var node; // check if it is a parenthesized expression
 
     if (state.token === '(') {
       // parentheses (...)
       openParams(state);
       getToken(state);
       node = parseAssignment(state); // start again
 
       if (state.token !== ')') {
         throw createSyntaxError(state, 'Parenthesis ) expected');
       }
 
       closeParams(state);
       getToken(state);
       node = new ParenthesisNode(node);
       node = parseAccessors(state, node);
       return node;
     }
 
     return parseEnd(state);
   }
   /**
    * Evaluated when the expression is not yet ended but expected to end
    * @return {Node} res
    * @private
    */
 
 
   function parseEnd(state) {
     if (state.token === '') {
       // syntax error or unexpected end of expression
       throw createSyntaxError(state, 'Unexpected end of expression');
     } else {
       throw createSyntaxError(state, 'Value expected');
     }
   }
   /**
    * Shortcut for getting the current row value (one based)
    * Returns the line of the currently handled expression
    * @private
    */
 
   /* TODO: implement keeping track on the row number
   function row () {
     return null
   }
   */
 
   /**
    * Shortcut for getting the current col value (one based)
    * Returns the column (position) where the last state.token starts
    * @private
    */
 
 
   function col(state) {
     return state.index - state.token.length + 1;
   }
   /**
    * Create an error
    * @param {Object} state
    * @param {string} message
    * @return {SyntaxError} instantiated error
    * @private
    */
 
 
   function createSyntaxError(state, message) {
     var c = col(state);
     var error = new SyntaxError(message + ' (char ' + c + ')');
     error.char = c;
     return error;
   }
   /**
    * Create an error
    * @param {Object} state
    * @param {string} message
    * @return {Error} instantiated error
    * @private
    */
 
 
   function createError(state, message) {
     var c = col(state);
     var error = new SyntaxError(message + ' (char ' + c + ')');
     error.char = c;
     return error;
   }
 
   return parse;
 });