How to make a calculator in PHP? - 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...

Answer 2

There is a Math Parser class called bcParserPHP that might be of interest.
Seems fairly simple to use and pretty powerful.
Example code from their site:
$parser = new MathParser();
$parser->setVariable('X', 5);
$parser->setVariable('Y', 2);
$parser->setExpression('COS(X)+SIN(Y)/2');
echo $parser->getValue();
Unfortunately, it's a commercial product; I don't know if that would stop you using it or not (guess it depends on the price and on your needs).
A non-commercial alternative might be this one: http://www.phpclasses.org/package/2695-PHP-Safely-evaluate-mathematical-expressions.html
Note that this class uses eval() internally, which I would avoid doing if possible.
Failing that, writing your own language parser would be the ideal solution, but not really sensible to do that in PHP.

Answer 3

I'd start by stripping the input of anything which shouldn't be in the expression (assuming you just want to allow add, subtract, multiply, divide, and no variables):
$expr = preg_replace('/[^0-9+*\/-]/', '', $expr);
and then, once I'm confident nothing dangerous remains in the user input, simply pass the itthrough eval() to evaluate the expression:
$result = eval("return $expr;");
No need to reinvent the wheel.
Edited to incorporate Kolink's corrections. Thanks!