Wie kann man in PHP als Strings übergebene mathematische Formeln sicher auswerten?

function calculator1($str){
    eval("$str = $str;");
    return $str;
}

function calculator2($str){
    $fn = create_function("", "return ({$str});" );
    return $fn();
};

class EvalMath {

    var $suppress_errors = false;
    var $last_error = null;

    var $v = array('e'=>2.71,'pi'=>3.14); // variables (and constants)
    var $f = array(); // user-defined functions
    var $vb = array('e', 'pi'); // constants
    var $fb = array(  // built-in functions
        'sin','sinh','arcsin','asin','arcsinh','asinh',
        'cos','cosh','arccos','acos','arccosh','acosh',
        'tan','tanh','arctan','atan','arctanh','atanh',
        'sqrt','abs','ln','log');

    function EvalMath() {
        // make the variables a little more accurate
        $this->v['pi'] = pi();
        $this->v['e'] = exp(1);
    }

    function e($expr) {
        return $this->evaluate($expr);
    }

    function evaluate($expr) {
        $this->last_error = null;
        $expr = trim($expr);
        if (substr($expr, -1, 1) == ';') $expr = substr($expr, 0, strlen($expr)-1); // strip semicolons at the end
        //===============
        // is it a variable assignment?
        if (preg_match('/^\s*([a-z]\w*)\s*=\s*(.+)$/', $expr, $matches)) {
            if (in_array($matches[1], $this->vb)) { // make sure we're not assigning to a constant
                return $this->trigger("cannot assign to constant '$matches[1]'");
            }
            if (($tmp = $this->pfx($this->nfx($matches[2]))) === false) return false; // get the result and make sure it's good
            $this->v[$matches[1]] = $tmp; // if so, stick it in the variable array
            return $this->v[$matches[1]]; // and return the resulting value
        //===============
        // is it a function assignment?
        } elseif (preg_match('/^\s*([a-z]\w*)\s*\(\s*([a-z]\w*(?:\s*,\s*[a-z]\w*)*)\s*\)\s*=\s*(.+)$/', $expr, $matches)) {
            $fnn = $matches[1]; // get the function name
            if (in_array($matches[1], $this->fb)) { // make sure it isn't built in
                return $this->trigger("cannot redefine built-in function '$matches[1]()'");
            }
            $args = explode(",", preg_replace("/\s+/", "", $matches[2])); // get the arguments
            if (($stack = $this->nfx($matches[3])) === false) return false; // see if it can be converted to postfix
            for ($i = 0; $i<count($stack); $i++) { // freeze the state of the non-argument variables
                $token = $stack[$i];
                if (preg_match('/^[a-z]\w*$/', $token) and !in_array($token, $args)) {
                    if (array_key_exists($token, $this->v)) {
                        $stack[$i] = $this->v[$token];
                    } else {
                        return $this->trigger("undefined variable '$token' in function definition");
                    }
                }
            }
            $this->f[$fnn] = array('args'=>$args, 'func'=>$stack);
            return true;
        //===============
        } else {
            return $this->pfx($this->nfx($expr)); // straight up evaluation, woo
        }
    }

    function vars() {
        $output = $this->v;
        unset($output['pi']);
        unset($output['e']);
        return $output;
    }

    function funcs() {
        $output = array();
        foreach ($this->f as $fnn=>$dat)
            $output[] = $fnn . '(' . implode(',', $dat['args']) . ')';
        return $output;
    }

    //===================== HERE BE INTERNAL METHODS ====================\

    // Convert infix to postfix notation
    function nfx($expr) {

        $index = 0;
        $stack = new EvalMathStack;
        $output = array(); // postfix form of expression, to be passed to pfx()
        $expr = trim(strtolower($expr));

        $ops   = array('+', '-', '*', '/', '^', '_');
        $ops_r = array('+'=>0,'-'=>0,'*'=>0,'/'=>0,'^'=>1); // right-associative operator?  
        $ops_p = array('+'=>0,'-'=>0,'*'=>1,'/'=>1,'_'=>1,'^'=>2); // operator precedence

        $expecting_op = false; // we use this in syntax-checking the expression
                                   // and determining when a - is a negation

        if (preg_match("/[^\w\s+*^\/()\.,-]/", $expr, $matches)) { // make sure the characters are all good
            return $this->trigger("illegal character '{$matches[0]}'");
        }

        while(1) { // 1 Infinite Loop ;)
            $op = substr($expr, $index, 1); // get the first character at the current index
            // find out if we're currently at the beginning of a number/variable/function/parenthesis/operand
            $ex = preg_match('/^([a-z]\w*\(?|\d+(?:\.\d*)?|\.\d+|\()/', substr($expr, $index), $match);
            //===============
            if ($op == '-' and !$expecting_op) { // is it a negation instead of a minus?
                $stack->push('_'); // put a negation on the stack
                $index++;
            } elseif ($op == '_') { // we have to explicitly deny this, because it's legal on the stack 
                return $this->trigger("illegal character '_'"); // but not in the input expression
            //===============
            } elseif ((in_array($op, $ops) or $ex) and $expecting_op) { // are we putting an operator on the stack?
                if ($ex) { // are we expecting an operator but have a number/variable/function/opening parethesis?
                    $op = '*'; $index--; // it's an implicit multiplication
                }
                // heart of the algorithm:
                while($stack->count > 0 and ($o2 = $stack->last()) and in_array($o2, $ops) and ($ops_r[$op] ? $ops_p[$op] < $ops_p[$o2] : $ops_p[$op] <= $ops_p[$o2])) {
                    $output[] = $stack->pop(); // pop stuff off the stack into the output
                }
                // many thanks: http://en.wikipedia.org/wiki/Reverse_Polish_notation#The_algorithm_in_detail
                $stack->push($op); // finally put OUR operator onto the stack
                $index++;
                $expecting_op = false;
            //===============
            } elseif ($op == ')' and $expecting_op) { // ready to close a parenthesis?
                while (($o2 = $stack->pop()) != '(') { // pop off the stack back to the last (
                    if (is_null($o2)) return $this->trigger("unexpected ')'");
                    else $output[] = $o2;
                }