How to Securely Evaluate Mathematical Strings in PHP Using Infix to Postfix Parsing?

Mathematical Evaluation of Strings Using Infix to Postfix Parsing

Mathematical evaluation of strings, such as "2-1" to produce "1," requires parsing the string into its constituent parts. In PHP, the default method for mathematical evaluation involves using the eval() function, which executes arbitrary PHP code and may introduce security vulnerabilities.

However, a more secure approach is to use an infix to postfix parser to convert the string into Reverse Polish Notation (RPN). An RPN solver can then evaluate the resulting expression without the need for eval().

Implementing an Infix to Postfix Parser

Below is an example of how to implement an infix to postfix parser using a PHP class:

class EOS {
  private $operators = ['+', '-', '*', '/', '^'];
  private $precedence = [
    '*' => 3,
    '/' => 3,
    '+' => 2,
    '-' => 2,
    '^' => 4
  ];

  public function solveIF($infix) {
    $postfix = $this->infixToPostfix($infix);
    return $this->postfixSolver($postfix);
  }

  // Converts infix expression to postfix
  private function infixToPostfix($infix) {
    $stack = new Stack();
    $postfix = '';
    $tokens = explode(' ', $infix);

    foreach ($tokens as $token) {
      if (in_array($token, $this->operators)) {
        while (!$stack->isEmpty() && $this->precedence[$stack->top()] >= $this->precedence[$token]) {
          $postfix .= $stack->pop() . ' ';
        }
        $stack->push($token);
      } else {
        $postfix .= $token . ' ';
      }
    }

    while (!$stack->isEmpty()) {
      $postfix .= $stack->pop() . ' ';
    }

    return $postfix;
  }

  // Solves postfix expression
  private function postfixSolver($postfix) {
    $stack = new Stack();
    $tokens = explode(' ', $postfix);

    foreach ($tokens as $token) {
      if (in_array($token, $this->operators)) {
        $operand2 = $stack->pop();
        $operand1 = $stack->pop();
        $result = $this->evaluateOperator($token, $operand1, $operand2);
        $stack->push($result);
      } else {
        $stack->push($token);
      }
    }

    return $stack->top();
  }

  // Evaluates operators
  private function evaluateOperator($op, $operand1, $operand2) {
    switch ($op) {
      case '+':
        return $operand1 + $operand2;
      case '-':
        return $operand1 - $operand2;
      case '*':
        return $operand1 * $operand2;
      case '/':
        return $operand1 / $operand2;
      case '^':
        return pow($operand1, $operand2);
    }
  }
}

Usage:

$eo = new EOS();
$result = $eo->solveIF("2-1");
echo $result; // Prints 1

Additional Alternatives:

While using an infix to postfix parser is a secure method for mathematical evaluation, there are additional alternatives available:

• Wolfram|Alpha API: Provides mathematical evaluation capabilities through an API.
• Sage: An open-source mathematical software system.
• PHP Dice Calc: A PHP library for mathematical operations.

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