exp4j

# Perfomance penalty of `java.util.Stack`

This is copy of the original [#26](https://github.com/fasseg/exp4j/issues/26) discussion

I've been profiling `exp4j` in particular `Expression.evaluate()`, from the profiling I gathered the following data (using Netbeans profiler):

```

Using Stack                 100.00%

evaluate()         19633    100.00%     

 Total Stack       10900     55.52%     

  Stack.pop()       5219     26.58%  

  Stack.push()      3361     17.12%

  Double.valueOf()  2320     11.82%  

 HashMap.get()      1479      7.53%

-----------------------------------

Using LinkedList             85.48%

evaluate()         16782    100.00%

 Total LinkedList   8938     53.26%

  LinkedList.push() 3670     21.87%

  LinkedList.pop()  2705     16.12%

  Double.valueOf()  2563     15.27%

 HashMap.get()      1493      8.90%

-----------------------------------

Using ArrayStack             46.45%

evaluate()          9120    100.00%

 Total ArrayStack    971     10.65%

  ArrayStack.push()  590      6.47%

  ArrayStack.pop()   381      4.18%

 HashMap.get()      1452     15.92%

```

The results show that most of the time used by `Expression.evaluate()` is wasted on the use of `java.util.Stack` which is backed by `java.util.Vector`.

I tested again using `java.util.LinkedList` which can be used as a drop in replacement for `java.util.stack`, it shows some improvements (~15%) but the boxing/unboxing process still takes up a lot of time.

Finally I've created a simple `ArrayStack` class that works with an array of doubles directly and doesn't need to box/unbox nor to adapt the methods from `java.util.Vector` to `push()` and `pop()`. The final result is that the `Expression.evaluate()` uses less than 50% of the time.

About the table:

The second column of the table is the total time in _ms_ used by the method in 1M excecutions.

The profiled code was:

``` java

public class Test {

    static final String EXPRESSION = "log(x) - y * sqrt(x^cos(y)) "

                                   + "+ 43 / 9 * sin(x) - 3 ^ (-3)";

    public static void main(String[] args) {

        final Expression expression = new ExpressionBuilder(EXPRESSION)

                .variables("x", "y")

                .build();

        Random rnd = new Random();

        double val = 0;

        int count = 0;

        while (count < 1000000) {

            expression.setVariable("x", rnd.nextDouble());

            expression.setVariable("y", rnd.nextDouble());

            val += expression.evaluate();

            count++;

        }

        System.out.println(val);

    }

}

```

Looking forward now most of the time seems to be used retrieving the variable values.