calc.js

/*
  E -> M [+ M]  
  M -> B [* B]
  B -> Num | (E)
*/

function calc(str){

  str = str.replace(/\s/g,'');
  var pos = 0;

  function whatNext(){
    if(pos >= str.length){
      return null;
    }else{
      return str[pos];
    }
  }

  function next(){
    var result = whatNext();
    pos++;
    return result;
  }

  function assertNext(s){
    if(s != whatNext()){
      throw new Error();
    }
  }

  function E(){
    var result = M();
    while(whatNext() == '+'){
      next();
      result += M();
    }
    return result;
  }

  function M(){
    var result = B();
    while(whatNext() == '*'){
      next();
      result *= B();
    }
    return result;
  }

  function B(){
    if(whatNext() == '('){
      next();
      var result = E();
      assertNext(')');
      next();
      return result;
    }else{
      return Num();
    }
  }

  function Num(){
    var numStr = '';
    var symbol;
    while(/[0-9]/.test(symbol = whatNext())){
      next();
      numStr += symbol;
    }
    if(numStr === ''){
      throw new Error('expected number');
    }else{
      return parseInt(numStr);
    }
  }

  var result = E();
  assertNext(null);
  return result;
}

calc('(((1 + 2 + 3)*4 + 1) * 10)')