implement calculator by js with BNF parser

index.js

DEBUG = false;
TEST = true;
noop = function() {};
log = assert = noop;
if (DEBUG) {
  log = console.log.bind(console);
}
if (TEST) {
  assert = function(a,b,m) { console.assert(a.toString() === b.toString(), m); };

  log('test lexer');
  assert(lexer('12'), [12]);
  assert(lexer('-  12  +  3'), ['-', 12, '+', 3]);
  assert(lexer('12+345-678*910'), [12, '+', 345, '-', 678, '*', 910]);

  log('test parser');
  assert(parser([12]), 12);
  assert(parser([1, '+', 2]), 3);
  assert(parser([12, '+', 3]), 15);
  assert(parser([12, '+', 345, '-', 678, '*', 910]), -616623);

  log('test all');
  assert(parser(lexer('4/2')), 2);
  assert(parser(lexer('4-23+5')), -14);
  assert(parser(lexer('12+345-678*910')), -616623);
  assert(parser(lexer('(2*3)/(2-1+1)+11')), 14);
}

function lexer(str) {
  var buf = [];
  var tmp = '';

  for (var i = 0; i < str.length; i++) {
    var c = str[i];
    if (c === ' ') continue;
    if (c === '+' || c === '-'
        || c === '*' || c === '/'
        || c === '(' || c === ')') {
          if (tmp) {
            // if tmp exists, that is a number
            // so push before operator
            buf.push(Number(tmp));
            tmp = '';
          }
          buf.push(c);
          continue;
        }
    tmp += c;
  }

  if (tmp) buf.push(Number(tmp));
  return buf;
}

function parser(lexed) {
  log(lexed);
  // expr : term { (+|-) term }
  // term : fact { (*|/) fact }
  // fact : number | '(' expr ')'
  function fact() {
    var c = lexed.shift(); log('1', c);
    if (typeof(c) === 'number') {
      return c;
    }
    if (c === '(') {
      c = expr(); log('2', c);
      if (lexed.shift() !== ')') throw 'invalid expr';
      return c;
    }
    throw 'invalid expr';
  }
  function term() {
    var c = fact(); log('3', c);
    while (lexed[0] === '*' || lexed[0] === '/') {
      var o = lexed.shift(); log('4', o);
      if (o === '*') c = c * term();
      if (o === '/') c = c / term();
    }
    return c;
  }
  function expr() {
    var c = term(); log('5', c);
    while (lexed[0] === '+' || lexed[0] === '-') {
      var o = lexed.shift(); log('6', o);
      if (o === '+') c = c + term();
      if (o === '-') c = c - term();
    }
    return c;
  }
  return expr();
}