evaluator.js/dist/evaluator.js

Evaluates mathematical expressions

var symbols = {
  '^': {
    infix: '_POW'
  },
  '*': {
    infix: '_MUL'
  },
  '/': {
    infix: '_DIV'
  },
  '%': {
    infix: '_MOD'
  },
  '+': {
    infix: '_ADD',
    prefix: '_POS'
  },
  '-': {
    infix: '_SUB',
    prefix: '_NEG'
  }
};

var factorial = function (x) { return x >= 0 ? x < 2 ? 1 : x * factorial(x - 1) : NaN; };

var operators = {
  '_POW': {
    name: 'Power',
    precedence: 4,
    associativity: 'right',
    method: function (x, y) { return Math.pow( x, y ); }
  },
  '_POS': {
    name: 'Positive',
    precedence: 3,
    associativity: 'right',
    method: function (x) { return x; }
  },
  '_NEG': {
    name: 'Negative',
    precedence: 3,
    associativity: 'right',
    method: function (x) { return -x; }
  },
  '_MUL': {
    name: 'Multiply',
    precedence: 2,
    associativity: 'left',
    method: function (x, y) { return x * y; }
  },
  '_DIV': {
    name: 'Divide',
    precedence: 2,
    associativity: 'left',
    method: function (x, y) { return x / y; }
  },
  '_MOD': {
    name: 'Modulo',
    precedence: 2,
    associativity: 'left',
    method: function (x, y) { return x % y; }
  },
  '_ADD': {
    name: 'Add',
    precedence: 1,
    associativity: 'left',
    method: function (x, y) { return x + y; }
  },
  '_SUB': {
    name: 'Subtract',
    precedence: 1,
    associativity: 'left',
    method: function (x, y) { return x - y; }
  }
};
var constants = {
  'E': Math.E,
  'LN2': Math.LN2,
  'LN10': Math.LN10,
  'LOG2E': Math.LOG2E,
  'LOG10E': Math.LOG10E,
  'PHI': (1 + Math.sqrt(5)) / 2,
  'PI': Math.PI,
  'SQRT1_2': Math.SQRT1_2,
  'SQRT2': Math.SQRT2,
  'TAU': 2 * Math.PI
};
var methods = {
  'ABS': function (x) { return Math.abs(x); },
  'ACOS': function (x) { return Math.acos(x); },
  'ACOSH': function (x) { return Math.acosh(x); },
  'ADD': function (x, y) { return x + y; },
  'ASIN': function (x) { return Math.asin(x); },
  'ASINH': function (x) { return Math.asinh(x); },
  'ATAN': function (x) { return Math.atan(x); },
  'ATANH': function (x) { return Math.atanh(x); },
  'ATAN2': function (y, x) { return Math.atan2(y, x); },
  'CBRT': function (x) { return Math.cbrt(x); },
  'CEIL': function (x) { return Math.ceil(x); },
  'COS': function (x) { return Math.cos(x); },
  'COSH': function (x) { return Math.cosh(x); },
  'DIVIDE': function (x, y) { return x / y; },
  'EXP': function (x) { return Math.exp(x); },
  'EXPM1': function (x) { return Math.expm1(x); },
  'FACTORIAL': factorial,
  'FLOOR': function (x) { return Math.floor(x); },
  'HYPOT': function () {
    var args = [], len = arguments.length;
    while ( len-- ) args[ len ] = arguments[ len ];

    return Math.hypot.apply(Math, args);
},
  'LOG': function (x) { return Math.log(x); },
  'LOG1P': function (x) { return Math.log1p(x); },
  'LOG10': function (x) { return Math.log10(x); },
  'LOG2': function (x) { return Math.log2(x); },
  'MAX': function () {
    var args = [], len = arguments.length;
    while ( len-- ) args[ len ] = arguments[ len ];

    return Math.max.apply(Math, args);
},
  'MEAN': function () {
    var args = [], len = arguments.length;
    while ( len-- ) args[ len ] = arguments[ len ];

    return [].concat( args ).reduce(function (sum, x) {
    return sum + x;
  }, 0) / [].concat( args ).length;
},
  'MIN': function () {
    var args = [], len = arguments.length;
    while ( len-- ) args[ len ] = arguments[ len ];

    return Math.min.apply(Math, args);
},
  'MOD': function (x, y) { return x % y; },
  'MULTIPLY': function (x, y) { return x * y; },
  'POW': function (x, y) { return Math.pow( x, y ); },
  'SIN': function (x) { return Math.sin(x); },
  'SINH': function (x) { return Math.sinh(x); },
  'SQRT': function (x) { return Math.sqrt(x); },
  'SUBTRACT': function (x, y) { return x - y; },
  'SUM': function () {
    var args = [], len = arguments.length;
    while ( len-- ) args[ len ] = arguments[ len ];

    return [].concat( args ).reduce(function (sum, x) {
    sum += x;
    return sum;
  }, 0);
},
  'TAN': function (x) { return Math.tan(x); },
  'TANH': function (x) { return Math.tanh(x); }
};

var isSymbol = function (token) { return Object.keys(symbols).includes(token); };

var isOperator = function (token) { return Object.keys(operators).includes(token); };

var isMethod = function (token) { return Object.keys(methods).includes(token); };

var isConstant = function (token) { return Object.keys(constants).includes(token); };

var isNumber = function (token) { return /(\d+\.\d*)|(\d*\.\d+)|(\d+)/.test(token); };

var isOpenParenthesis = function (token) { return /\(/.test(token); };

var isCloseParenthesis = function (token) { return /\)/.test(token); };

var isComma = function (token) { return /,/.test(token); };

var isWhitespace = function (token) { return /\s/.test(token); };

var round = function (number, precision) {
  var modifier = Math.pow( 10, precision );
  return !modifier ? Math.round(number) : Math.round(number * modifier) / modifier;
};

function topOperatorHasPrecedence(operatorStack, currentOperatorName) {
  if (!operatorStack.length) { return false; }
  var topToken = operatorStack[operatorStack.length - 1];
  if (!isOperator(topToken)) { return false; }
  var topOperator = operators[topToken];
  var currentOperator = operators[currentOperatorName];
  if (currentOperator.method.length === 1 && topOperator.method.length > 1) { return false; }
  if (topOperator.precedence > currentOperator.precedence) { return true; }
  return topOperator.precedence === currentOperator.precedence && topOperator.associativity === 'left';
}

function determineOperator(token, previousToken) {
  if (previousToken === undefined || isOpenParenthesis(previousToken) || isSymbol(previousToken) || isComma(previousToken)) {
    return symbols[token].prefix;
  }

  if (isCloseParenthesis(previousToken) || isNumber(previousToken) || isConstant(previousToken)) {
    return symbols[token].infix;
  }

  return undefined;
}
/**
 * Takes a string and parses out the array of tokens in infix notation.
 *
 * @param {string} expression The string.
 *
 * @throws {Error} No input.
 *
 * @returns {string[]} The array of tokens in infix notation.
 */


function parse(expression) {
  if (!expression.length) {
    throw Error('No input');
  }

  var pattern = /(\d+\.\d*)|(\d*\.\d+)|(\d+)|([a-zA-Z0-9_]+)|(.)/g;
  var infixExpression = (expression.match(pattern) || []).filter(function (token) { return !isWhitespace(token); }).map(function (token) { return token.toUpperCase(); });
  return infixExpression;
}
/**
 * Takes an array of tokens in infix notation and converts it to postfix notation.
 *
 * @param {string[]} infixExpression The array of tokens in infix notation.
 *
 * @throws {Error} No valid tokens.
 * @throws {Error} Misused operator: <token>.
 * @throws {Error} Mismatched parentheses.
 * @throws {Error} Invalid token: <token>.
 * @throws {Error} Insufficient arguments for method: <token>.
 *
 * @returns {string[]} The array of tokens in postfix notation.
 */


function convert(infixExpression) {
  if (!infixExpression.length) {
    throw Error('No valid tokens');
  }

  var operatorStack = [];
  var arityStack = [];
  var postfixExpression = [];
  var methodIsNewlyDeclared = false;
  infixExpression.forEach(function (token, index) {
    if (methodIsNewlyDeclared && !isOpenParenthesis(token)) {
      throw Error(("Misused method: " + (operatorStack[operatorStack.length - 1])));
    }

    methodIsNewlyDeclared = false;

    if (isMethod(token)) {
      methodIsNewlyDeclared = true;
      operatorStack.push(token);
      arityStack.push(1);
      return;
    }

    if (isConstant(token)) {
      postfixExpression.push(token);
      return;
    }

    if (isNumber(token)) {
      postfixExpression.push(parseFloat(token));
      return;
    }

    if (isSymbol(token)) {
      var operatorName = determineOperator(token, infixExpression[index - 1]);
      var operator = operators[operatorName];

      if (operator === undefined) {
        throw Error(("Misused operator: " + token));
      }

      while (topOperatorHasPrecedence(operatorStack, operatorName)) {
        postfixExpression.push(operatorStack.pop());
      }

      operatorStack.push(operatorName);
      return;
    }

    if (isOpenParenthesis(token)) {
      operatorStack.push(token);
      return;
    }

    if (isComma(token)) {
      arityStack[arityStack.length - 1] += 1;

      while (!isOpenParenthesis(operatorStack[operatorStack.length - 1])) {
        if (!operatorStack.length) {
          throw Error('Invalid token: ,');
        }

        postfixExpression.push(operatorStack.pop());
      }

      return;
    }

    if (isCloseParenthesis(token)) {
      while (!isOpenParenthesis(operatorStack[operatorStack.length - 1])) {
        if (!operatorStack.length) {
          throw Error('Mismatched parentheses');
        }

        postfixExpression.push(operatorStack.pop());
      }

      operatorStack.pop();

      if (isMethod(operatorStack[operatorStack.length - 1])) {
        var method = operatorStack[operatorStack.length - 1];
        var argumentCount = arityStack.pop();

        if (argumentCount < methods[method].length) {
          throw Error(("Insufficient arguments for method: " + method));
        }

        postfixExpression.push(((operatorStack.pop()) + ":" + argumentCount));
      }

      return;
    }

    throw Error(("Invalid token: " + token));
  });

  while (operatorStack.length) {
    var operator = operatorStack[operatorStack.length - 1];

    if (isOpenParenthesis(operator) || isCloseParenthesis(operator)) {
      throw Error('Mismatched parentheses');
    }

    postfixExpression.push(operatorStack.pop());
  }

  return postfixExpression;
}
/**
 * Takes an array of tokens in postfix notation and resolves the result.
 *
 * @param {string[]} postfixExpression The array of tokens in postfix notation.
 *
 * @throws {Error} No operations.
 * @throws {Error} Insufficient arguments for method: <token>.
 * @throws {Error} Insufficient operands for operator: <token>.
 * @throws {Error} Division by zero.
 * @throws {Error} Insufficient operators.
 *
 * @returns {number} The result.
 */


function resolve(postfixExpression) {
  if (!postfixExpression.length) {
    throw Error('No operations');
  }

  var evaluationStack = [];
  postfixExpression.forEach(function (token) {
    if (isMethod(String(token).split(':')[0])) {
      var ref = token.split(':');
      var methodName = ref[0];
      var argumentCount = ref[1];
      var method = methods[methodName];
      var isVariadic = method.length === 0;
      var requiredArguments = isVariadic ? 1 : method.length;

      if (evaluationStack.length < requiredArguments) {
        throw Error(("Insufficient arguments for method: " + token));
      }

      var result$1 = method.apply(void 0, evaluationStack.splice(isVariadic ? -argumentCount : -method.length));
      evaluationStack.push(result$1);
      return;
    }

    if (isConstant(token)) {
      evaluationStack.push(constants[token]);
      return;
    }

    if (isNumber(token)) {
      evaluationStack.push(token);
      return;
    }

    var operator = operators[token];

    if (evaluationStack.length < operator.method.length) {
      throw Error(("Insufficient operands for operator: " + (operator.name)));
    }

    if (token === '_DIV' && evaluationStack[evaluationStack.length - 1] === 0) {
      throw Error('Division by zero');
    }

    var result = operator.method.apply(operator, evaluationStack.splice(-operator.method.length));
    evaluationStack.push(result);
  });

  if (evaluationStack.length > 1) {
    throw Error('Insufficient operators');
  }

  var reduction = evaluationStack[0];
  var result = round(reduction, 8);
  return result;
}
/**
 * Takes a string and evaluates the result.
 *
 * @param {string} expression The string.
 *
 * @throws {Error} No input.
 * @throws {Error} No valid tokens.
 * @throws {Error} Misused operator: <token>.
 * @throws {Error} Mismatched parentheses.
 * @throws {Error} Invalid token: <token>.
 * @throws {Error} No operations.
 * @throws {Error} Insufficient arguments for method: <token>.
 * @throws {Error} Insufficient operands for operator: <token>.
 * @throws {Error} Division by zero.
 * @throws {Error} Insufficient operators.
 *
 * @returns {number} The result.
 */


function index (expression) {
  try {
    var infixExpression = parse(expression);
    var postfixExpression = convert(infixExpression);
    var result = resolve(postfixExpression);
    return result;
  } catch (error) {
    throw error;
  }
}

module.exports = index;
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