How to make a calculator in PHP?

Question

I want to use PHP to calculate simple algebraic expressions like, 8*(5+1), entered via an <input> tag by a normal user (which means, normal notation: no syntax changes like Multiply(8, Add(5, 1))). Also, it has to show all steps, but that's not hard. The problem, right now, is calculating the value of the expressions.

Note: this is what I thought so far, which is quite inefficient but it's a provisory solution. Just replace strings where possible: in our example, recognize the string 5+1 and replace it with 6. Then, loop again, replace (6) with 6, loop again, and replace 8*6 with 48. The code for multiplying, for example, should look like this:

for ($a=1; $a < 1000; $a++) {
    for ($b=1; $b < 1000; $b++) {
        string_replace($a . '*' . $b, $a*$b, $string);
    }
}

Answer 1

Depending on your needs, I would suggest looking into the Shunting Yard Algorithm. It's pretty easy to implement, and works quite well.

Here's an example I whipped up a while ago: GIST.

Here's the code copy/pasted into one block:

Expression Definitions:

class Parenthesis extends TerminalExpression {

    protected $precidence = 7;

    public function operate(Stack $stack) {
    }

    public function getPrecidence() {
        return $this->precidence;
    }

    public function isNoOp() {
        return true;
    }

    public function isParenthesis() {
        return true;
    }

    public function isOpen() {
        return $this->value == '(';
    }

}

class Number extends TerminalExpression {

    public function operate(Stack $stack) {
        return $this->value;
    }

}

abstract class Operator extends TerminalExpression {

    protected $precidence = 0;
    protected $leftAssoc = true;

    public function getPrecidence() {
        return $this->precidence;
    }

    public function isLeftAssoc() {
        return $this->leftAssoc;
    }

    public function isOperator() {
        return true;
    }

}

class Addition extends Operator {

    protected $precidence = 4;

    public function operate(Stack $stack) {
        return $stack->pop()->operate($stack) + $stack->pop()->operate($stack);
    }

}

class Subtraction extends Operator {

    protected $precidence = 4;

    public function operate(Stack $stack) {
        $left = $stack->pop()->operate($stack);
        $right = $stack->pop()->operate($stack);
        return $right - $left;
    }

}

class Multiplication extends Operator {

    protected $precidence = 5;

    public function operate(Stack $stack) {
        return $stack->pop()->operate($stack) * $stack->pop()->operate($stack);
    }

}

class Division extends Operator {

    protected $precidence = 5;

    public function operate(Stack $stack) {
        $left = $stack->pop()->operate($stack);
        $right = $stack->pop()->operate($stack);
        return $right / $left;
    }

}

class Power extends Operator {

    protected $precidence=6;

    public function operate(Stack $stack) {
        $left = $stack->pop()->operate($stack);
        $right = $stack->pop()->operate($stack);
        return pow($right, $left);
    }
}

abstract class TerminalExpression {

    protected $value = '';

    public function __construct($value) {
        $this->value = $value;
    }

    public static function factory($value) {
        if (is_object($value) && $value instanceof TerminalExpression) {
            return $value;
        } elseif (is_numeric($value)) {
            return new Number($value);
        } elseif ($value == '+') {
            return new Addition($value);
        } elseif ($value == '-') {
            return new Subtraction($value);
        } elseif ($value == '*') {
            return new Multiplication($value);
        } elseif ($value == '/') {
            return new Division($value);
        } elseif ($value == '^') {
            return new Power($value);
        } elseif (in_array($value, array('(', ')'))) {
            return new Parenthesis($value);
        }
        throw new Exception('Undefined Value ' . $value);
    }

    abstract public function operate(Stack $stack);

    public function isOperator() {
        return false;
    }

    public function isParenthesis() {
        return false;
    }

    public function isNoOp() {
        return false;
    }

    public function render() {
        return $this->value;
    }
}

The stack (really simple implementation):

class Stack {

    protected $data = array();

    public function push($element) {
        $this->data[] = $element;
    }

    public function poke() {
        return end($this->data);
    }

    public function pop() {
        return array_pop($this->data);
    }

}

And finally, the executor class:

class Math {

    protected $variables = array();

    public function evaluate($string) {
        $stack = $this->parse($string);
        return $this->run($stack);
    }

    public function parse($string) {
        $tokens = $this->tokenize($string);
        $output = new Stack();
        $operators = new Stack();
        foreach ($tokens as $token) {
            $token = $this->extractVariables($token);
            $expression = TerminalExpression::factory($token);
            if ($expression->isOperator()) {
                $this->parseOperator($expression, $output, $operators);
            } elseif ($expression->isParenthesis()) {
                $this->parseParenthesis($expression, $output, $operators);
            } else {
                $output->push($expression);
            }
        }
        while (($op = $operators->pop())) {
            if ($op->isParenthesis()) {
                throw new RuntimeException('Mismatched Parenthesis');
            }
            $output->push($op);
        }
        return $output;
    }

    public function registerVariable($name, $value) {
        $this->variables[$name] = $value;
    }

    public function run(Stack $stack) {
        while (($operator = $stack->pop()) && $operator->isOperator()) {
            $value = $operator->operate($stack);
            if (!is_null($value)) {
                $stack->push(TerminalExpression::factory($value));
            }
        }
        return $operator ? $operator->render() : $this->render($stack);
    }

    protected function extractVariables($token) {
        if ($token[0] == '$') {
            $key = substr($token, 1);
            return isset($this->variables[$key]) ? $this->variables[$key] : 0;
        }
        return $token;
    }

    protected function render(Stack $stack) {
        $output = '';
        while (($el = $stack->pop())) {
            $output .= $el->render();
        }
        if ($output) {
            return $output;
        }
        throw new RuntimeException('Could not render output');
    }

    protected function parseParenthesis(TerminalExpression $expression, Stack $output, Stack $operators) {
        if ($expression->isOpen()) {
            $operators->push($expression);
        } else {
            $clean = false;
            while (($end = $operators->pop())) {
                if ($end->isParenthesis()) {
                    $clean = true;
                    break;
                } else {
                    $output->push($end);
                }
            }
            if (!$clean) {
                throw new RuntimeException('Mismatched Parenthesis');
            }
        }
    }

    protected function parseOperator(TerminalExpression $expression, Stack $output, Stack $operators) {
        $end = $operators->poke();
        if (!$end) {
            $operators->push($expression);
        } elseif ($end->isOperator()) {
            do {
                if ($expression->isLeftAssoc() && $expression->getPrecidence() <= $end->getPrecidence()) {
                    $output->push($operators->pop());
                } elseif (!$expression->isLeftAssoc() && $expression->getPrecidence() < $end->getPrecidence()) {
                    $output->push($operators->pop());
                } else {
                    break;
                }
            } while (($end = $operators->poke()) && $end->isOperator());
            $operators->push($expression);
        } else {
            $operators->push($expression);
        }
    }

    protected function tokenize($string) {
        $parts = preg_split('((\d+|\+|-|\(|\)|\*|/)|\s+)', $string, null, PREG_SPLIT_NO_EMPTY | PREG_SPLIT_DELIM_CAPTURE);
        $parts = array_map('trim', $parts);
        return $parts;
    }

}

It works by first tokenizing the input (based on word boundary, and tokens). Then, it runs the Shunting Yard algorithm on it to convert the input into a RPN (Reverse Polish Notation) stack. Then, it's just a matter of executing the stack. Here's a quick example:

$math = new Math();

$answer = $math->evaluate('(2 + 3) * 4');
var_dump($answer);
// int(20)

$answer = $math->evaluate('1 + 2 * ((3 + 4) * 5 + 6)');
var_dump($answer);
// int(83)

$answer = $math->evaluate('(1 + 2) * (3 + 4) * (5 + 6)');
var_dump($answer);
// int(231)

$math->registerVariable('a', 4);
$answer = $math->evaluate('($a + 3) * 4');
var_dump($answer);
// int(28)

$math->registerVariable('a', 5);
$answer = $math->evaluate('($a + $a) * 4');
var_dump($answer);
// int(40)

Now, this example is significantly more complex than you may need. The reason is that it also handles grouping and operator precedence. But it's a decent example of a running algorithm that doesn't use EVAL and supports variables...